Croquembouche Cone

Combine milk, butter, and salt in a medium saucepan. Scrape vanilla seeds into the mixture. Bring to a simmer over medium heat, about 10 minutes.

Meanwhile, whisk egg yolks and sugar in a separate bowl until pale and light, about 3 minutes, and whisk in cornstarch until combined.

Slowly add the hot simmered milk to the egg yolks, whisking constantly to temper the yolks. Pour tempered mixture back into the pan and cook, whisking constantly, until custard is thick and holds whisk marks, about 2 minutes. Strain custard through a fine-mesh strainer, discard vanilla bean pods, and place plastic wrap directly on the surface of the custard. Refrigerate for at least 2 hours.

Preheat the oven to 425 degrees F (220 degrees C). Line 5 or 6 rimmed baking sheets with parchment paper.

Combine milk, water, 1 cup plus 2 tablespoons butter, sugar, and salt in a large saucepot over medium heat; bring to a boil, then immediately remove from heat and add the flour all at once. Stir slowly at first to combine, then vigorously until mixture forms a uniform paste.

Transfer paste to the bowl of a stand mixer fitted with a paddle attachment. Add 12 eggs, 1 at a time, blending on low speed until each egg is completely incorporated. Mixture may appear broken, but keep stirring until it is glossy, smooth, and stretchy.

Transfer dough into a pastry bag fitted with a 1/2-inch tip and pipe 1 1/2-inch puffs about 1 inch apart on the prepared baking sheets to get about 20 per sheet. Use a wet finger to smooth the tops. Beat the final egg with a splash of water in a small bowl; brush the tops of the puffs with egg wash.

Place 2 to 3 baking sheets in the preheated oven and bake puffs for 15 minutes. Do not open the oven door, or the puffs will deflate. Decrease oven temperature to 350 degrees F (175 degrees C) and bake until deeply golden brown, about 10 minutes more. Remove puffs from oven and place sheet on a wire rack to cool.

Increase oven temperature to 425 degrees F (220 degrees C) to continue baking remaining puffs.

Make caramel while puffs cool. Bring sugar, water, and corn syrup to a boil in a medium saucepan over medium-high heat. Swirl pan occasionally to help dissolve the sugar, but do not stir, until syrup turns deep amber, about 20 minutes. Meanwhile, prepare a large bowl of ice water.

While the caramel is cooking, fit a pastry bag with a small round tip and fill with pastry cream. Poke a hole in the bottom of each puff and gently pipe in pastry cream to fill. Do not do this far in advance as puffs will begin to turn soggy once filled.

As soon as caramel has turned a deep amber color, place the bottom of the pot into the ice water to stop the cooking and firm the caramel, about 30 seconds. Carefully pour the still-hot caramel into a 2-cup glass measuring cup.

Trace a circle onto a piece of parchment using an 8-inch round cake pan. Cut out the circle, leaving a 1-inch border, and place on a serving platter.

Dip 1 side of a puff into the caramel and stick it onto the parchment. Dip another puff on 2 sides, then stick 1 side to the parchment and the other to its neighboring puff. Repeat gluing puffs over the parchment circle to form a sturdy base, then continue building a conical tower of increasingly smaller circles. Top the tower with a single puff. If caramel begins to harden, microwave for 20 to 30 seconds to loosen.

Let any unused caramel cool in the pan until it forms a thread when lifted with a fork. Dip the tip of a fork into the caramel and quickly wave it in circles around the tower to create a web of caramel strands. Repeat as desired. Crack the caramel web and dismantle the tower to serve.