Preheat your oven to 400°F and line two baking sheets with parchment paper. Unfold the puff pastry sheets and cut each one into thirds along the natural fold lines, then cut those strips in half so you end up with 12 even rectangles total.
Using a sharp knife, score a border about half an inch in from the edge of each rectangle, going all the way around without cutting through the dough. This creates a raised, puffy edge once it bakes. Use a fork to prick the center area a few times so it doesn't balloon up in the oven.
Whisk the egg and milk together in a small bowl until combined. Brush this mixture along just the scored border of each pastry rectangle. This step gives the edges that glossy, golden-brown color you see in bakery pastries.
Spoon about two teaspoons of blackberry jam into the center of each rectangle and spread it gently within the scored border. Scatter a small handful of fresh blueberries evenly over the jam on each piece.
Place the trays in the oven and bake for 15 to 20 minutes, until the blueberries have burst slightly and the pastry has puffed up into deep golden layers. Keep an eye on them after the 15-minute mark since ovens vary.
As soon as the tarts come out of the oven, sprinkle the toasted almonds over the top while everything is still warm. Let the tarts cool completely on a rack before adding the glaze, otherwise the glaze will just melt right off.
Whisk together the powdered sugar, heavy cream, lemon juice, and lemon zest until smooth. It should be thick but still pourable. Drizzle it generously over the cooled tarts and let it set for a few minutes before serving.