Combine the ice water and buttermilk in a small pitcher and chill until needed. In the bowl of a food processor (or in a large bowl), combine the sweet rice, oat, and millet flours with the cornstarch, tapioca flour, ground chia seed, sugar, and salt. Scatter the ghee over the top in teaspoon-sized lumps and chill until the ghee is very firm, 20-30 minutes or longer. Place the lid on the food processor, but don’t process yet! Simultaneously pour the cold buttermilk mixture through the feed tube in a slow and steady stream while pulsing the food processor all the while until all the liquid is added and the butter is broken down into chunks of varying sizes from tiny peas to lima beans. The dough should hold together when squeezed; if it needs more liquid to come together, gently pulse in a tablespoon or two more ice water.
Press the dough into a ball, flatten into a disc in a large piece of plastic wrap or beeswax wrap, wrap tightly, and chill until firm, at least 1 hour and up to 3 days.
Let the dough soften at room temperature for 10 – 20 minutes to make it easier to roll. On a surface dusted lightly with oat flour, roll the chilled dough out into a rough square that is about ¼-inch thick. As you work, dust the top of the dough with oat flour, using a dry pastry brush to sweep away the excess. When the dough begins to stick to the work surface, use a bench scraper to move it to one side, dust the surface with more flour, and return the dough to the floured surface to continue rolling. Don’t worry if the dough crumbles and wants to fall apart, just press it back together. Once the dough is rolled out, fold it in thirds like folding a letter, then roll it up from a skinny end into a loose spiral. Gently press to flatten it slightly, and chill for 30 minutes. Optionally (preferably), repeat this step once more. The dough will get smoother and easier to work with as you make these turns, and the finished dough will be super flaky and tender. At this point the dough can be chilled for up to 2 days, or sealed and frozen for up to 1 month.
Position a rack in the lower third of the oven and preheat to 400ºF. If you have a pizza stone, place it on the rack. Have a 10-inch solid ceramic tart pan or 9- or 10-inch pie pan ready, and place it on a rimmed baking sheet. (I don’t recommend using a loose-bottom tart pan in case of leaky custard.)
If the dough is very firm, let stand at room temperature until slightly softened, 5 minutes in a warm kitchen or 15 minutes in a cool kitchen. On a surface dusted lightly with oat flour, roll the dough out into a 13- or 14-inch round, dusting the dough and surface with more flour to prevent sticking. Lift the dough into the tart or pie pan and ease it into the corners letting the excess hang over the sides of the pan. Trim the edges to an even 1-inch overhang, and, if using a tart pan, fold the edges over to make a crust. If using a pie pan, fold the edges under and crimp the edges. Prick the bottom of the crust all over with the tines of a fork, and chill until firm, 30 minutes or longer.
Line the bottom and sides of the crust with a piece of parchment paper and fill all the way to the top with dry beans or (preferably) pie weights, pressing the weights gently into the sides of the crust. Bake the crust until the edges are golden, 20-25 minutes. Carefully remove the pie weights (I use a large spoon to scoop them into a bowl) and gently peel away the parchment. Return the crust to the oven and bake until the bottom is dry and slightly golden, 8-12 more minutes.
While the crust bakes, prepare the vegetables:
Halve the leeks lengthwise and slice crosswise about ¼ inch thick. Place in a bowl filled with cool water and let sit, separating the rings and swirling them to oust any sandy dirt from between the layers. Slice one third of the mushrooms lengthwise about ½-inch thick (to decorate the top of the quiche), and cut the rest into ¾-inch cubes. Snap or peel the ends from the asparagus, reserve 7 or 8 pretty slender stalks for the top of the quiche, and cut the rest into 1-inch pieces.
Heat 1 tablespoon of the ghee in a wide skillet set over medium-low heat. Add the mushroom slices and a big pinch of salt and cook until golden on both sides, about 10 minutes, turning occasionally. Remove from the pan and add the rest of the ghee. Add the leeks and cook, stirring frequently, until tender, 5 minutes. Add the diced mushrooms and ¼ teaspoon salt, reduce the heat to medium-low, and cook, stirring occasionally, until the mushrooms have softened, 5-10 minutes, adding the wine in splashes when the pan looks dry. Add the cut asparagus and cook until crisp-tender, another 5 minutes. Deglaze with the rest of the wine, letting it cook off completely. Remove from the heat.
Make the custard:
Place the eggs, sweet rice flour, cream, milk, salt, and pepper in a blender and blend until smooth. (Alternatively, whisk the eggs with the flour until smooth, then whisk in the cream, milk, salt, and pepper, and strain the mixture to remove any lumps of flour.)
Assemble and bake the quiche:
Scatter the cheese over the bottom of the parbaked crust. Top with the cooked asparagus mixture, then pour in as much custard as will fit – you may have some leftover. Lay the asparagus spears over the top in a decorative pattern, and top with the cooked mushroom slices. Sprinkle with a bit of salt and pepper.
Carefully transfer the quiche to the oven and bake until golden, slightly puffed, and set when you give it a wiggle, 25-35 minutes. Remove from the oven and let cool slightly, then cut into wedges and serve. The best way to cut this quiche is to use a small serrated knife to saw through the toppings first, then cut the wedges through the rest of the way. Serve warm or at room temperature. Extra quiche keeps well, refrigerated airtight, for up to 3 days. Reheat before serving.
Notes
Be sure to give yourself lots of time to chill, roll, form, and parbake the crust – or better yet, make the dough the day before and let it rest overnight.Folding the pie dough in the manner of puff pastry helps create a smoother dough that's easier to work with and holds together beautifully, and the baked crust is extra tender and flaky to boot. I often make a double batch of dough and store the excess in the freezer for the next pie adventure.Nutritional values are based on one of eight servings.