Preheat the oven to 350 F and get out a baking sheet and line with parchment paper.
Take the thawed sheet of puff pastry dough and lay it out on a flat, lightly floured surface. Using a knife or pizza cutter, cut the dough into three rectangles, on the fold lines that are already in the dough. Then cut each rectangle into 4 even pieces, so you end up with 12 even little rectangles total.
Place them on a baking sheet and bake in the preheated oven for 18 minutes, until puffed up and golden brown. Watch carefully so they don't burn. Remove from the oven to cool.
While the puffs are cooling, make the whipped cream. In a large mixing bowl, pour in whipping cream and beat with the whip attachment or hand mixer until the cream starts to thicken. Add the vanilla and sugar and continue beating until soft peaks form. Keep going until it is slightly firmer. The whipped cream should just be able to hold its shape on a spoon.
After the little puffs have cooled, use a small knife to cut each of the lpuffs in half, so you will now have 24 halves total. Each Blackberry Napoleon will use three half pieces each, so this recipe will make a total of 8 desserts.
Place the apricot preserves into a small microwave safe bowl. Microwave for about 15-20 seconds to soften the preserves. Pour the preserves into a plastic sandwich bag (or pastry bag), push down into one corner, and snip a small hole in the corner to allow squeezing out the preserves.
On the serving plate or platter, place one bottom half, cut side up. Spread on about 2 tablespoons of whipped cream, and top with 6 blackberries.
Place a half piece on top of the blackberries and repeat a second layer of whipped cream and blackberries.
Crown with a top half piece, sprinkle on a dash of powdered sugar and drizzle on some apricot preserves. Serve right away.
Substitute 2 pints of your favorite berries for the blackberries.
Non-Dairy whipped topping can be substituted for the whipping cream