How to Make It
Make the crust: Preheat oven to 450°F. Line a large baking sheet with parchment paper.
Combine 1 cup water, butter, sugar, and salt in a large saucepan. Bring to a boil over medium-high; reduce heat to medium. Add flour all at once, and stir vigorously with a wooden spoon until a tight dough forms and pulls away from sides of pan, about 2 minutes. Remove from heat, and transfer dough to bowl of a stand mixer fitted with the paddle attachment.
Beat on medium speed 1 minute to help release steam. Add eggs, 1 at a time, beating until incorporated after each addition. Beat until dough is thick and glossy, about 1 minute.
Place dough on prepared baking sheet; spread into a 13- x 9 1/2-inch rectangle, leaving 1/2-inch of parchment paper exposed around edges. Bake in preheated oven until golden brown, 20 to 25 minutes. Let cool completely, about 1 hour.
Make the custard: Meanwhile, whisk together sugar and cornstarch in a heavy saucepan; whisk in milk and eggs until smooth. Bring to a boil over medium, whisking constantly, until mixture reaches a chilled pudding–like consistency, 8 to 10 minutes. Boil, whisking constantly, 1 minute. Remove from heat; whisk in cream cheese and vanilla until smooth. Pour through a fine wire-mesh strainer into a bowl; discard solids. Let strained custard cool to room temperature, about 1 hour. Spread custard on cooled crust.
Make the whipped cream: Place mascarpone, heavy cream, and powdered sugar in bowl of a stand mixer fitted with the whisk attachment. Beat on medium speed until soft peaks form, 2 to 3 minutes.
Assemble the cake: Spread whipped cream evenly over custard. Garnish with chocolate shavings. Chill, uncovered, until cold, 1 to 2 hours. Cut into squares just before serving.