In a sauce pan. Add pitted cherries, sugar, lemon juice cornstarch, almond extract and mix. Add water and mix everything together. Heat the sauce pan to low-medium. Bring it to a light simmer then turn down the heat to low. Cook for 5-8 minutes or until the sauce thickens and cherries are soft. Make sure be gentle while stirring the entire time with a wooden spoon. Remove from heat source and let cool. Add more sugar or lemon juice if needed.
Preheat the oven to 400°F. Place parchment paper on a baking sheet.
Place flour on a working surface (this will help prevent the puff sheets from sticking to the working surface). Unfold the puff sheet. Cut the dough into 3 long pieces. Then cut long pieces in half. Transfer 6 rectangle pastry to the baking sheets. Repeat the other pastry.
Egg wash: In a small bowl: combine egg, water and whisk.
Brush the egg wash on around the edges of the pastries. Then, divide the cherry filling (I added 8 cherries into each) into 6 pastry. Place the other 6 rectangle pastry on top of the cherry filling. Use a fork and seal the dough edges together. Slice 2-3 slit to each pastry. Brush the egg wash on top. Sprinkle sugar on top of the pastry.
Bake for 20-25 minutes or until golden. Remove from the oven and let rest for 15 minutes before serving.