3/4-inch round cutter; about a 16-inch foam cone, covered with foil
Arrange a rack in the middle of the oven and preheat to 375 degrees F. Line a baking sheet with parchment paper.
For the craquelin: Add the butter and sugar to a stand mixer bowl fitted with the paddle attachment and beat until combined. Add the flour and beat to combine. Stir in a few drops of food coloring of choice and beat until uniform in color. Scoop the paste out onto a sheet of parchment paper with a rubber spatula. Cover with another piece of parchment paper and use your hands to press out into an even sheet. Then roll gently a few times with a rolling pin to flatten to an even 1/8-inch thick. Transfer to a baking sheet and freeze for 20 minutes. When the craquelin is frozen, remove it from the freezer. Peel the top piece of parchment off and cut rounds with a 3/4-inch round cutter.
For the choux dough: Meanwhile, combine the butter, sugar, salt and 2 cups water in a medium saucepan over low heat. Once the butter has melted, bring it to a boil over medium heat. As soon as it boils, remove the pan from the heat and sift the flour directly into the pan. Stir the mixture into a paste with a wooden spoon; you will have to beat it hard. Return the pan to medium heat. Stir the batter continuously until it pulls away from the sides of the pan and is slightly shiny, about 3 minutes.
Transfer the batter to a stand mixer bowl fitted with the paddle attachment and beat until slightly cooled, about 3 minutes. Add the eggs, one at a time, incorporating each one thoroughly before adding the next.
Fit a large pastry bag with a plain round tip and fill with the choux dough. Pipe twelve 2-inch circular mounds, about 2 inches apart, onto the prepared baking sheet. If the batter has a peak, dab it smooth with a wet fingertip.
Beat the egg yolk with 1 tablespoon water and brush the surface of the puffs with the beaten yolk. Using a small offset spatula, gently lift the craqulin rounds off the parchment and place on top of the cream puffs. Bake on the middle rack for 20 minutes, then reduce the oven temperature to 325 degrees F and continue baking until the puffs are golden brown, light, airy and crisp, 30 to 35 more minutes. If the cream puffs still don't feel completely dry and crisp at the end of the baking time, poke a hole in the bottom with a paring knife and place them back into the oven for a few more minutes to crisp up. Remove from the oven and cool completely on a wire rack.
Fill a pastry bag with a small plain tip with the Vanilla Pastry Cream. Fill each puff with the pastry cream from the hole in the bottom.
To assemble: Mix the sugar, corn syrup and 1 cup water together in a heavy-bottomed pot and bring to a boil. Continue to boil until it reaches the hard crack stage at 300 degrees F.
Use the hot syrup to adhere the puffs to about a 16-inch foam cone covered in foil, or pile up to form a mound. If the hard candy caramel gets too thick, heat it gently.
Whisk together the sugar, cornstarch and salt in a saucepan. Add the milk, eggs and vanilla bean seeds and whisk to combine. Turn the heat to medium-high.Whisk often to keep it from sticking to the bottom of the pan. Once thick, after about 10 minutes, turn off the heat, add the butter and stir until combined.
Pour the pastry cream into a bowl and cover with plastic wrap directly on the surface. Place in the fridge to cool completely, about 2 hours.