For the Italian Custard Cream, put the milk and vanilla in a saucepan and bring to a simmer over medium heat. In a bowl, whip together the sugar, flour, and egg yolks with a hand mixer. Ladle a cup of the milk-vanilla mixture into the bowl and beat to temper the yolks. Add the yolk mixture to the pot and beat over medium heat with the hand mixer until thick and creamy, about 1 minute. As you are beating, move the pot on and off the flame so that you don’t scramble the eggs.
Remove the pot from the heat, add the butter, and whip for 2 minutes to thicken the cream. Transfer to a bowl. Let cool, cover with plastic wrap, and refrigerate at least 6 hours. Will keep for up to 1 week. To make chocolate custard cream, add 1 1/2 ounces melted, cooled unsweetened chocolate along with the butter. For a richer chocolate flavor, add a little more.
To make the Italian Whipped Cream, put the cream and sugar in a bowl and whip on high speed with a hand mixer. Do not overmix or you’ll end up with butter. The cream can be refrigerated in an airtight container for up to 3 days. Whisk by hand to refresh before using.
To make Lobster Tail Cream for the Croquembouche, put the custard cream in a mixing bowl. Add the whipped cream, a little at a time, folding it in with a rubber spatula. The cream can be refrigerated in an airtight container for up to 4 days. Whisk briefly by hand to refresh before using.
To make the Cream Puff Shells, position a rack in the center of the oven and preheat the oven to 450 degrees. Put 1 cup water, the butter and salt in a heavy saucepan and bring to a boil over high heat. Add the flour and stir with a wooden spoon until the ingredients come together into a smooth, uniform dough, approximately 2 minutes. Transfer the mixture to the bowl of a stand mixer fitted with the paddle attachment. (If you don’t have a stand mixer you can use a hand mixer fitted with the blending attachments.) Start paddling on low speed, then add the eggs, 1 at a time, until thoroughly absorbed, mixing for 1 minute between each egg, and stopping the motor periodically to scrape down the sides and bottom of the bowl with a rubber spatula. Finish with the final egg and mix for an additional 2 minutes. (Use the dough immediately. It does not refrigerate well.)
Transfer the dough into a pastry bag fitted with #6 plain tip. Pipe rounds on 2 nonstick baking trays, about 2 inches in diameter by about 1/2-inch high, leaving 2 inches between each puff. You should be able to make 24 puffs.
Bake the puffs in the oven, in batches if necessary, until golden brown, 15 to 20 minutes.
Remove the tray from the oven and let the puffs cool in the tray for 20 minutes. The puffs can be kept in an airtight container at room temperature for up to 2 days before filling and serving.
To assemble the Croquembouche, put the Lobster Tail Cream in a large mixing bowl. Put 2 tablespoons of the espresso in a small heatproof bowl and add 2 tablespoons of hot water. Stir them together into a paste then whisk the paste into the lobster tail cream. Taste, and if desired, make more paste with equal parts espresso powder and hot water and whisk into the cream for a stronger espresso flavor.
Fill the puffs: Use your pinkie to hollow out the puffs from the bottom. Put a few cups of cream into a pastry bag fitted with the #7 star tip, and pipe cream into the puffs from the bottom, refilling the bag with cream as you run out.
Pipe some of the cream into the center of each of 6 small dessert plates. Arrange 3 cream puffs around the cream and 1 cream puff on top. Working with 1 plate at a time on a turntable, pipe more cream over and around the cream puffs. Turning the turntable, use a cake spatula to smooth the cream and completely encase the cream puffs. Sprinkle a teaspoon of espresso powder over each dessert and finish by garnishing with chocolate shavings.