Have a 10-inch (25 cm) oven-proof skillet at the ready.
Place the chilled dough on a sheet of parchment paper lightly dusted with oat flour, letting it soften for 5 minutes if it’s too firm to roll out. Roll the dough out into an 11-inch (28 cm) round, dusting the dough as you work. If it begins to stick to the parchment, top it with a second piece of parchment, grasp the whole thing and bravely flip it over. Peel away the top piece of parchment and continue rolling. If the dough tears or cracks, just squish it back together. The dough round will be about ¼” thick or a little shorter. Invert the pan over the dough round and cut the dough ¼” wider than the pan. Slip the dough round, parchment and all, onto a baking sheet and chill until firm while you prepare the apples. (The dough can be covered and stored for up to 1 day.)
Meanwhile, fill a medium bowl with cool water and add the lemon juice and the lemon. Peel the apples, quarter, and cut out the cores and stems, dropping the quarters into the acidulated water as you work.
Melt the butter and salt in the skillet over a medium flame. Add the ½ cup of sugar to the butter and simmer, stirring occasionally, until the sugar begins to melt and take on some color, about 2 minutes. Swirl in the calvados and continue cooking, stirring frequently, until the mixture bubbles thickly, 3-5 minutes. It will be beige in color, but don’t worry, it will caramelize later.
Remove the pan from the heat. Drain the apples well. Carefully place the apples with a cut side down in concentric circles, beginning with the outside, with the fat ends facing out. Really pack them in; they will lose volume as they cook so we want as many as possible in there. It’s ok if they don’t all quite fit in a single layer; they can be nestled in as they simmer. Sprinkle the apples with the remaining 2 tablespoons of sugar.
Position a rack in the center of the oven and preheat to 400ºF (205ºC).
Return the pan to a medium flame and simmer until the juices bubble up thickly around the apples and look slightly golden, 20-25 minutes. Remove the pan from the heat again. Remove the dough round from the refrigerator, place a large cutting board on top, flip the whole thing over, and remove the parchment paper. Use the board to slide the dough round atop the apples and carefully tuck the edges down around the apples, being careful not to burn yourself on the hot pan and using a spoon to tuck the dough in if needed. This will form a lip when the tart is inverted and prevent the juices from gushing everywhere.
Place the pan in the oven and bake until the pastry is deeply golden all over, 20-30 minutes. Let cool 1 minute, then use a thin knife or small, offset spatula to loosen the edges of the tart dough and apples. Place a large platter or cutting board over the tart and, wearing oven mitts, grasp it all with your hands and flip the whole thing over. Remove the pan. If apples have stuck to the pan, use a knife or offset spatula to spackle them back onto the tart.
Cut the tart into wedges and serve warm with vanilla or crème fraiche ice cream. The tart is best the day of baking and will keep at room temperature for 1 day. Leftovers can be refrigerated airtight for up to several days; reheat before serving for best results.