Make the Pastry Cream and Rough Puff Pastry.
In the bowl of a stand mixer fitted with a whisk, whip the heavy cream until almost stiff peaks form. Gently fold the whipped cream into the 3/4 cup pastry cream until combined. Refrigerate until ready to use.
Lightly flour your work surface, and gently roll out the puff pastry into a 11 in [28 cm] square. Using a pastry cutter, cut 1 in [25 mm] strips from each side of the square and set aside; you will have 4 strips total. Transfer the square of puff pastry to a parchment-lined sheet pan.
Pierce the square of puff pastry all over with the tines of a fork. Lightly brush the dough edges with the egg wash, being very careful not to let any drip down the sides, as this can hinder the puff pastry from rising. Lay the reserved 1 in [25 cm] strips over the edges of each square so they line up exactly, overlapping at the corners, and trim them as necessary.
Refrigerate the puff pastry for 30 minutes while the oven preheats.
Preheat the oven to 400 [200 C]. Remove the pastry from the refrigerator, and brush the tops of each pastry strip with the egg wash, again being careful not to let any drip down the sides. Bake the puff pastry until light brown and puffed, about 15 minutes. Using an offset spatula or the back of a spoon, press down on the center of the pastry, leaving the borders puffed up. Return to the oven, and bake 10 to 12 minutes more, until deep golden brown. Transfer the tart to a wire rack to cool, and press down the center again if needed. Let the tart cool completely before filling.
When the tart has cooled, fill the center of the square with the pastry cream filling, and then top with the fresh raspberries.