Preheat oven to 400 degrees Fahrenheit. Peel, core, and slice 2 pounds apples; set aside.
Place 1 sheet puff pastry on a piece of wax paper, and roll into a circle the size of your pan; chill in fridge. Put cast-iron or other ovenproof pan on stove. Coat bottom and sides of pan with just enough butter to leave a film. Add ¼ cup brown sugar. Add apple slices in a concentric circle, starting with outside of pan; make 2 layers of apples. Turn heat to medium-high, and cook for 20 minutes.
Transfer to oven, and cook 20 minutes more. Remove and place puff pastry over apples. Bake 30 minutes more or until golden.
Remove from oven; cool for 15–20 minutes. Invert pan onto platter, and serve.