Preheat oven to 375°F (190°C). Grease a 9-inch tart pan with butter or cooking spray and set aside.
In a large bowl, combine the flour and salt. Add in the cubed butter and mix with a pastry blender or your fingertips until the mixture resembles coarse crumbs. Add in the ice water and mix until the dough just comes together. Do not overmix. Wrap the dough in plastic wrap and chill in the refrigerator for at least 30 minutes.
On a lightly floured surface, roll out the dough into a 12-inch circle. Carefully transfer the dough to the prepared tart pan. Trim off any excess dough, then prick the bottom of the dough with a fork.
In a large bowl, combine the sliced apples, granulated sugar, light brown sugar, cinnamon, and nutmeg. Mix until the apples are evenly coated with the sugar mixture.
Arrange the apples in a circular pattern in the tart pan, slightly overlapping each slice. Start from the outside and work your way in. When you reach the center, arrange the remaining slices in a rose shape.
Bake for 40-45 minutes, until the crust is golden brown and the apples are tender. If the crust starts to get too brown, cover it with a piece of aluminum foil.
Let the tart cool for 10 minutes before removing from the pan. Dust with powdered sugar, if desired, and serve warm.