This classic French upside-down apple tart is named for the Tatin sisters, who served it at their hotel in the Loire Valley. When the tart is turned out of the skillet, the top crust—an overlapping ring of golden, caramelized apples—is an enticing sight. Prepare the tart in any deep, heavy ovenproof skillet, such as cast-iron, measuring 7 to 8 inches across the bottom and 10 to 11 inches across the top. Pans made especially for tarte Tatin are available online and at some cookware stores. Please read Rolling Pie Dough and Lining a Pie or Tart Pan with Dough.
Have ready:
Roll or cut the dough into a 12-inch round, slip a cookie sheet beneath it, and refrigerate.
Position a rack in the upper third of the oven. Preheat the oven to 375°F.
Peel, core, and quarter:
Melt in a skillet (see note for skillet size and type):
Remove from the heat and sprinkle evenly over the bottom:
Arrange a ring of apple quarters around the outer edge of the skillet, standing the apples on the thin edge of their cut side and propping them up against one another so as to fit as many as possible. Fill in the center of the skillet with the remaining apple quarters. (You may have a piece or two of apple left over.) Place the skillet over high heat and cook until the juices turn from butterscotch to deep amber, 10 to 12 minutes.
Remove the skillet from the heat, spear the apples with a fork or the tip of a paring knife, and flip them onto their uncooked sides. Return the skillet to high heat and cook 5 minutes more. Remove the skillet from the heat and slide the prepared crust onto the apples. Being careful not to burn your fingers, gently tuck the edges of the dough against the inner sides of the skillet. Transfer to the oven and bake until the crust is richly browned, 25 to 35 minutes. Let cool on a rack for 20 minutes.
Loosen the sides of the tart with a knife and invert the tart onto a heatproof serving plate. Return any apples that stick to the skillet to their proper place on top of the tart. Serve immediately, or let stand at room temperature for up to 8 hours. When ready to serve, warm the tart to tepid in an oven heated at the lowest setting.