Slice apples into ½-inch slices. Remove the core and seeds.
Place 8 pats of butter (¼ tablespoon each) on a baking sheet. Top each pat of butter with about 1 teaspoon brown sugar and ¼ teaspoon cinnamon.
Place 5–8 apple slices over each butter mixture, overlapping them slightly.
Cut the puff pastry into 8 rectangles. Place one rectangle of puff pastry over each apple stack, then gently press the edges down with a fork to seal.
Bake at 400°F for 20–25 minutes, until the puff pastry is golden brown. Carefully flip each pastry over so the caramelized apples are on top, then bake for another 3–5 minutes.
Serve warm for the best flavor.