Preheat the oven to 400 degrees F. Line an 18-by-13-inch baking sheet with parchment paper. Have another 18-by-13-inch baking sheet and piece of parchment on hand.
Roll out the puff pastry to a 12-by-15-inch rectangle. Cut in three equal rectangles, about 12 by 5 inches each. Dock all over with a fork to suppress the puff pastry's rise in the oven. Transfer the pieces to the prepared baking sheet, cover with the other sheet of parchment and top with the second baking sheet. Bake until the flour structure has set and the pastry looks light golden and flaky, 10 to 12 minutes. Remove the top baking sheet and piece of parchment and return to the oven until golden brown, 4 to 5 minutes more. Cool completely on a baking rack.
Meanwhile, combine the granulated sugar, salt, vanilla and 2 1/2 cups of the milk in a large saucepan. Cook over medium-high heat until bubbles form around the edges. While the milk is warming, whisk together the cornstarch, flour, eggs and remaining 1/2 cup milk in a large bowl.
Temper the egg mixture with the hot milk mixture, adding a ladleful to the egg mixture at a time, whisking the whole time. Once you've added two-thirds of the milk mixture to the egg mixture, pour it back into the pan and cook on medium heat, whisking constantly. Once the mixture thickens and comes to boil, stir vigorously and count to 60. Remove from the heat.
Pass the pastry cream through a fine-mesh sieve into a bowl, then stir in the butter and Scotch. Cool over an ice bath, stirring occasionally, until the pastry cream reaches room temperature. Transfer the pastry cream to a pastry bag fitted with a medium round tip. (Or, if not using immediately, cover with plastic wrap, pressing the plastic wrap onto the surface of the pastry cream to keep a skin from forming.)
Whip the cream in a medium bowl with a hand mixer or balloon whisk until medium-stiff peaks form. Put the whipped cream in a separate pastry bag with a medium round tip.
Add the white chocolate chips and 1 tablespoon of the corn syrup to a metal bowl set over a pan of simmering water (do not let the bowl touch the water) and heat until melted and smooth; stir to combine. Add the semisweet chocolate chips and remaining 1 tablespoon corn syrup to a separate metal bowl over a pan of simmering water. Heat until melted and smooth, then stir to combine.
Trim the cooled puff pastry carefully with a serrated knife to produce three identical pieces. Lay down one piece of pastry on a serving plate and pipe a layer of pastry cream on top. Sprinkle with chocolate crumbs. Top with a second layer of pastry and pipe a layer of whipped cream on top. Sprinkle with sliced almonds. Dip the top of the third layer of pastry in the melted semisweet chocolate, then spread with a knife to smooth the top. Top the whipped cream layer with the chocolate-covered pastry. Drizzle on some of the white chocolate with a spoon and create a swirled pattern with a wooden skewer if desired.
This recipe has been updated and may differ from what was originally published or broadcast.