Preheat the oven to 400 degrees F.
Let the puff pastry sit and thaw for 40 minutes. While it is sitting, Mix the almond paste, butter, and sugar.
Unfold the puff pastry and set one sheet aside. With the beaten egg and pastry brush, brush a 3 x 3 grid of 1" lines onto the sheet so that you have 9 squares of equal size of pastry outlined, plus all outer edges of the dough should be brushed as well. This doesn't have to be perfect.
Place 1/2 tablespoon of almond paste mixture in the center of each square.
Lay the second sheet of unfolded puff pastry on top of the first sheet with the almond dollops. With your fingers, press the puff pastry together firmly around the outer seams and along each line of egg. You won't be able to see the egg wash as you have laid the second pastry sheet on top, but make your best guess to recreate the grid with your finger pressings.
Cut into 9 equal squares, along the egg seams. Brush each individual pastry with egg and top with almonds.
Bake for 25 minutes.