Defrost 1 sheet of puff pastry. If there are creases in your pastry roll it out gently to get rid of the creases and make sure all areas are pliable and the same thickness.
Cut the sheet of pastry into quarters.
On each square of pastry make 4 long cuts, each 1" in from the edge. Two adjacent cuts should connect and the opposite two should connect. However, there corners in between the two sets that connect, should stay in tact.
Essentially you are cutting a 1" frame but two opposing corners should stay intact connecting the frame to the center piece.
Brush the 1" frame with a little water, I usually use my finger for this part. Pick up one corner of the frame (where the corners connect) and fold it over the center piece. Line the corner up with the opposing corner of the center piece and press down gently.
Repeat with the opposing connected corner.
Carefully place each of the four tarts on the parchment lined baking sheet.
Evenly divide the frangipane into the centers of the tarts, spread into an even layer inside of the frame. It will seem like a lot of filling and should be tall but don't let it reach over the pastry frame.
Brush the frames with heavy cream and then sprinkle on the sliced almonds.
Place 5-6 wedges of plums in two rows onto the frangipane centers, stagger them so more will fit.
Place in the preheated oven to bake for 15 minutes. After the timer goes off, rotate the pan 180 degrees. Then bake for another 15 minutes until slightly golden brown on top.
Remove the pan from the oven and place on a wire rack to cool.
Brush the plums with the almond simple syrup.
Allow the tarts to cool for at least 10 minutes and then dust with powdered sugar.
Store leftovers in an airtight container.
To re-crisp, heat the oven to 375 F and bake for 5-10 minutes until the pastry has become crisp again.