Preheat oven to 400 degrees. Line two baking sheets with parchment paper.
Unfold 1 puff pastry sheet. On a lightly floured surface or parchment paper, roll the pastry into a 14-by-12-inch rectangle.
Cut slits 1 inch apart from the 2 sides of the pastry rectangle leaving about 4 inches down the length of the rectangle for the fillings.
Spread half of almond pastry filling lengthwise down the center of the pastry. Spoon half of jam over the top of the almond filling.
Starting at one end, fold the pastry strips over the filling on a diagonal, alternating sides to make a braid.
Press the ends of the strips down firmly.
Repeat the entire process with the second pastry sheet and the remaining almond paste and jam.
Place each braid on a parchment lined baking sheet.
Mix together the egg and heavy cream to make an egg wash.
Brush the puff pastries with the egg wash. Then top with sliced almonds.
Bake for 10 minutes at 400 degrees, then reduce the oven temperature to 350 degrees and bake for about 20-25 more minutes or until tops are lightly browned.
Cool for 10 minutes.
Mix together sifted confectioners sugar, vanilla extract and 2 tablespoons heavy cream until smooth. It may be necessary to add a little more cream to get the glaze to the perfect drizzling consistency. Drizzle glaze over the puff pastry braids.