Heat cherry juice, cornstarch, and sugar in a saucepan and let simmer for five minutes. Add the cherries and stir well.
Roll out the puff pastry and cut it into eight equal rectangles. Using a small bottle cap, make a row of three holes, one below the other, on four of the rectangles.
Mix the almonds, powdered sugar, almond extract, and vanilla extract together in a bowl. Knead the ingredients together until you have a cohesive mound of marzipan.
Roll out the marzipan and cut it into four small sheets. Place one sheet on top of each of the puff pastry rectangles without holes. Add some of the cherry mixture onto the marzipan, and cover with the puff pastry pieces with holes.
Seal the edges together by pressing them with a fork. Brush your pastries with egg and bake for 25 minutes at 350° F.