Melt the butter in a skillet over medium-high heat. Toss in the apple slices, brown sugar and cinnamon and cook over medium heat until the apples begin to caramelize or begin to get glazed with the sugar and butter.
Roll out the puff pastry in a freeform shape. Roll in the outer edge about a half inch to form a crust. Spread the warm apples on top of the pastry. Brush the crust with the lightly beaten egg and sprinkle with the granulated sugar. Bake for 20 to 30 minutes or until golden.