Split the vanilla bean down the center and use the back of a knife to scrape away the seeds. Set the seeds aside to use in the cake, and place the pod in a large saucepan. Use a vegetable peeler (t-shaped works the besto pare away 5 strips of lemon peel and add them to the pot. Juice the lemon and add the juice to the pot along with the water, vermouth or wine, and sugar. Bring the liquid to a boil while you prepare the quince.
Use a t-shaped vegetable peeler to pare away the skin of a quince. Cut it in half, leaving the seeds in, and add it to the pot. Continue with the remaining quince. Place a small, heat-proof plate over the quince to keep them submerged, cover partially with the lid of the pot, and adjust the flame to keep the liquid at a simmer. Cook until the quince are rosy and tender, about 1 1/2 hours, adding more water as needed to keep the quince submerged. When done, carefully remove the quince and let them drain, reserving the liquid (or let the quince cool in their juices if using later.) Core the quinces and cut them into 1/4" slices.
Return the poaching liquid to the saucepan and simmer until reduced by about half and bubbling thickly, about 10-20 minutes. Reserve.
Make the cake:
Position a rack in the center of the oven and preheat to 350º.
Shove a piece of parchment paper into an 8 or 9" round pan and trim the edges to rise 1" above the pan. Grease the bottom and sides with the 1 T of softened butter. Lay the quince slices, slightly overlapping, in concentric circles over the buttered parchment and set aside. If you have quince left over, chop them coarsely and set them aside to add to the batter. (I had about 1/2 a cup.)
Make the cake batter:
In the bowl of a stand mixer fitted with the paddle attachment (or in a large bowl fitted with your arm and a wooden spoon), combine the stick of butter, vanilla bean seeds, and sugar. Beat on medium speed until light and fluffy, 3 minutes. Add the eggs one at a time, beating until combined after each and scraping down the sides and bottom of the bowl as needed, then beat in the grated ginger.
Meanwhile, sift the sweet rice, oat, and millet flours with the baking powder and salt into a medium bowl.
With the mixer on low, stir half of the flour mixture into the butter mixture until just combined. Stir in the crème fraîche until just combined, then the rest of the flour, scraping down the sides and bottom of the bowl as needed. Stir in the chopped quince, if using, and give the batter a final stir by hand to make sure it is well-combined.
Spread the batter over the quinces evenly.
Bake the cake until the top is golden and a toothpick inserted near the center comes out clean, or a with a few moist crumbs, 40-50 minutes. Let the cake cool completely, then invert onto a serving platter and peel away the parchment. If the reduced poaching liquid has solidified, warm it in a small saucepan until liquid. Brush some of this glaze over the top of the cake. Serve the cake at room temperature. I like it with a flowery tea, such as Darjeeling. Extras will keep at room temperature for a day or two, or in the refrigerator for a few days.
Notes
The ginger here adds a subtle, floral warmth that accentuates the quince. For an extra-gingery version, try adding a few tablespoons of finely chopped candied ginger to the batter (decreasing the sugar a bit if you like).If making this for highly sensitive gluten-intolerant folks, be sure to seek out certified gluten-free ingredients, particularly oat flour (which you can also grind from gluten-free oats). If gluten isn't an issue, feel free to try this with all-purpose wheat flour, or other flours of your liking such as rye or barley. I haven't tried this with gluten-free all-purpose blends, but King Arthur and Cup 4 Cup are probably good bets if you'd prefer that route.I especially liked the quince that I cooked with Sutton Cellar's dry white vermouth, but the ones made with sauvignon blanc were also excellent; I think Lillet would be lovely, as well. The alcohol all cooks off, but you could also leave it out if you preferred, using extra water or fruit juice instead.This cake is a little bit fussy, so here are a few tips to ensure success:-Be sure to grease the parchment paper, otherwise the quince may stick to it, making it difficult to remove and marring the surface of the cake.-Don't overwork the batter, lest it become gummy from the sweet rice flour.-Let the cake cool before turning it out. This allows the cake time to gain structure, keeping it fluffy when inverted.Nutritional values are based on one of eight servings.