Tangy creme fraiche and fragrant vanilla bean perk up the whipped cream sandwiched between layers of puff pastry and strawberries in this towering summer dessert.
Preheat oven to 375 degrees. Sprinkle work surface with some of granulated sugar. Unfold dough on top and sprinkle with more granulated sugar. If necessary, roll out to a 9 1/2-by-12 1/2-inch rectangle, slightly more than 1/8 inch thick. Using a sharp knife or pastry cutter, cut into a 9-by-12-inch rectangle. Transfer to a baking sheet; freeze 20 minutes. Cut into twelve 4-by-2 1/4-inch rectangles. Transfer to two baking sheets and refrigerate until firm, about 30 minutes.
Prick rectangles all over with a fork. Coat two wire racks with cooking spray and place one over each set of rectangles (if you only have one cooling rack, work in batches). Bake until pastry just reaches tops of racks, about 15 minutes (do not let it bake into racks and stick). Remove racks; continue to bake until golden and evenly browned, about 15 minutes more. Let cool completely on racks, about 30 minutes.
With a mixer, whisk cream, creme fraiche, vanilla seeds, and confectioners' sugar on medium speed until stiff peaks form, 1 to 2 minutes. Fit a pastry bag with a large star tip (such as Ateco #825). Split pastry rectangles horizontally (to create 24 pieces total). Choose 8 nice tops; set aside. Arrange a single layer of strawberries over 8 bottom rectangles. Pipe about 2 tablespoons cream over berries. Top with a second layer of berries. Pipe 2 tablespoons cream onto 8 more rectangles. Top with a layer of strawberries. Pipe a dollop of cream onto bottom and place on top of first layer, pressing very gently to help stick. Pipe a dollop of cream on bottom of reserved rectangles and place on top, sugared-sides up. Refrigerate at least 1 hour and up to overnight.
If the berries are too tart, add a tablespoon or two more sugar to the cream mixture.