Place butter, sugar, and salt in an 8-inch cast iron skillet (a number 8 skillet) over medium heat. As sugar begins to melt, stir gently until everything is completely melted. Reduce heat to medium-low and cook until caramel is a deep brown, about 5 minutes. Remove from heat.

Place apple halves in the caramel sauce, stem side up, tightly packed and arranged in concentric circles.

Place the pan back over medium heat, and cook until the bottoms of the apples are caramelized and soft. Use a fork to turn over and continue cooking until apples are tender and completely caramelized, about 45 to 60 minutes.

Let cool to room temperature.

Preheat oven to 375°F.

If there's more than 1/2-inch of juice in the pan, carefully pour off some into a small saucepan. You can boil this into a syrup to drizzle over the tarte when serving.

Roll dough into a circle about 1 inch larger than the cast iron pan. Place over the apples and tuck the excess crust down along the sides.

Bake until crust is golden brown and crisp, about 25 minutes.

Let cool 15 minutes, then invert onto a plate.