In a 9-inch cast-iron skillet, melt butter over medium heat. Sprinkle 1/2 cup sugar evenly into the pan.
Arrange the apples in the pan. Increase the heat slightly, so the sugar simmers, and cook until the liquid in the pan is caramelized, 25 to 30 minutes. Transfer to a 425 F oven and bake until the apples are tender, about 15 minutes.
Unfold 1 sheet of puff pastry on a lightly floured surface. Place a plate on top and trim around the edges to make a pastry round; refrigerate until the apples are done.
Position the pastry over the apples and bake until deep golden and crisp, 15 to 20 minutes; let cool for 20 minutes before inverting onto a rimmed platter.
Whip the heavy cream with the 1 tsp sugar until soft peaks form; serve with the tart.