Preheat the oven to 400°F. Line a rimmed baking sheet with parchment and set aside.
Make the frangipane by adding the almonds and sugar to a food processor and pulsing until it’s very finely ground. Add in the butter and whip until mixture is well combined and fluffy.
Scrape the sides of the food processor down and add the almond extract, 1 egg, flour, and salt and pulse again to combine.
Unroll the sheets of puff pastry and cut each sheet into 4 even squares. Place them on the baking sheet about an inch apart.
Add about 1 tablespoon of the almond frangipane to the center of each pastry square and spread over the square, leaving about a 1/2-inch border around all sides.
Beat the remaining egg in a small bowl and brush the borders of the pastry squares.
Arrange about 6-8 plum slices on top of the frangipane of each square.
Bake for about 20 minutes, until the squares are puffed and golden-brown.