A traditional French croquembouche (third from left) is built from profiteroles filled with passion-fruit custard; it has a halo of spun sugar. Freeze the extra puffs for another time; fill them with any custard or creamy filling.
Heat oven to 400 degrees. Line three baking sheets with parchment paper; set aside.
In a medium saucepan, combine milk, butter, salt, and 1/2 cup water. Bring to a boil over medium-high heat; stir in the flour. Stir constantly until the mixture pulls away from the sides of the pan and becomes stiff, about 5 minutes. Remove from heat; transfer to the bowl of an electric mixer. Using the paddle attachment, mix on low speed about 1 minute. With mixer running, add eggs, one at a time, beating well between each addition. Transfer to a pastry bag fitted with a 1/4-inch plain round tip.
In a small bowl, combine the egg yolk with the heavy cream for an egg wash. Pipe about 50 puffs onto each sheet. Gently brush the puffs with the egg wash. Bake until puffs are golden brown, about 15 minutes. Transfer to a wire rack to cool.
Using a toothpick, poke a hole just large enough to fit the pastry tip in the bottom of each puff. Fill puffs with passion- fruit mousse by inserting the tip of the filled pastry bag into the hole. Place the filled puffs onto a baking sheet; place in refrigerator until ready to use.
Prepare nougat base and triangles; set aside. Trace the bottom of a 5-inch tart pan on a piece of lightly oiled parchment; set aside. Prepare the caramel; using hot caramel, attach the nougat triangles at a 25-degree angle to the base's edge, forming a crown. Working quickly, partially dip the filled puffs one at a time in the caramel, then adhere one puff to the next. Using the puffs, build an 8-inchtall cone-shaped tower; its base should be inside the parchment circle (you build it on the parchment so the hot caramel does not melt the crown). You will use about 80 puffs. Transfer completed tower to the nougat crown. Decorate with spun sugar and a tuile banner.