Add the apple slices to the pan. Then add the brown sugar, granulated sugar, cinnamon, and a pinch of salt. Gently stir until everything melts and is bubbling.
Cook to cook the apples over medium heat for about 10 minutes or until the apples are tender and coated in caramel. Keep a close eye on the mixture so the caramel doesn't burn. Then remove them from the heat and allow them to cool for a few minutes.
Roll the puff pastry sheet out on a lightly floured surface. Cut into 6 rectangles.
Place a sheet of parchment paper on the baking sheet.
Cut 3 tablespoons of butter into 6 pats. Place them evenly spaced on the parchment paper.
Place four apple slices on to p of each pat of butter.
Then place a rectangle of puff pastry on top of each set of apples. Use a fork to push down the edges of the puff pastry.
Bake for 30 minutes or until the puff pastry has puffed up and is golden.
Let the tarts cool for a few minutes before carefully flipping them over onto a plate.
Dust with powdered sugar and top with vanilla ice cream or whipped cream, if desired.
Notes
Storage: Cover cooled tarts tightly with plastic wrap or store in an airtight container. Keep in the refrigerator for up to 3 days.