1. Freeze 1 cup cut-up butter 30 minutes. Pulse cold butter, flour, salt, and 1/4 cup sugar in a food processor 7 to 8 times or until mixture resembles coarse meal. Add 1/2 cup ice-cold water, 1 Tbsp. at a time, and pulse just until mixture comes together and a dough forms. Turn dough out onto a piece of plastic wrap, and shape into a disk. Wrap in plastic wrap, and chill 2 to 24 hours.
2. Gently stir together apples, 1/2 cup butter, and remaining 1 1/2 cups sugar in a large bowl. Place apple mixture in a 10-inch cast-iron skillet. (Skillet will be very full.) Cook over medium-low heat 1 hour to 1 hour and 15 minutes or until liquid is reduced, thickened, and turns golden, stirring only once every 15 minutes. (Depending on your stovetop, you might need to lower the temperature if mixture begins to scorch on the bottom.)
3. Preheat oven to 425°. Unwrap dough, and turn out onto a lightly floured surface. Roll dough to a 12-inch circle; place over warm apple mixture, tucking edges into sides of skillet.
4. Bake at 425° for 25 minutes or until crust is golden brown and flaky. Let cool 10 minutes. Run a knife around edge of skillet; invert tart onto a cutting board or serving plate.