Make the pastries: Line a baking sheet with parchment paper. Unfold the puff pastry onto the prepared baking sheet. Whisk the egg yolk with 1 tablespoon water in a small bowl; brush all over the puff pastry, then sprinkle with the sugar. Freeze until the pastry is firm, 15 to 20 minutes.
Meanwhile, make the strawberry filling: Mash 1 cup strawberries with a fork in a large bowl. Add the remaining strawberries, 2 tablespoons sugar and the vanilla; toss to coat. Set aside until ready to assemble. Preheat the oven to 375 degrees F. Spread the almonds on a baking sheet and bake until golden, 5 to 7 minutes; set aside. Cut the puff pastry into four 4-inch squares with a sharp knife; prick all over with a fork. Transfer to the oven and bake until puffed and lightly golden, about 20 minutes. Reduce the oven temperature to 325 degrees F and continue baking until flaky and golden brown, about 15 more minutes. Remove to a rack and let cool completely.
Make the prosecco cream: Combine the mascarpone, heavy cream, the remaining 2 tablespoons sugar and the prosecco in a medium bowl; beat with a mixer on medium speed until soft peaks form, about 2 minutes. (Do not overbeat or the cream will become grainy.) Slice the pastries in half horizontally using a serrated knife. Put a bottom half on each plate. Top each with some prosecco cream and strawberries with their juices; cover with the top pastry halves and sprinkle with the almonds. Photograph by Anna Williams