Step 1

Preheat oven to 425˚. Line a rimmed baking sheet with parchment paper. Heat milk, butter, granulated sugar, salt, and ½ cup water in a medium saucepan over medium, stirring occasionally to melt butter. As soon as butter is melted, add flour all at once and stir with a wooden spoon, carefully at first to incorporate, then vigorously, until dough forms a single mass. Continue stirring, slapping dough against sides of saucepan with spoon, until dough leaves a thick film on bottom of pan and pulls away from sides, about 3 minutes (the important thing here is to cook the flour and dry out the dough). Transfer to a medium bowl and let rest 3 minutes.

Step 2

Using a wooden spoon, mix 5 eggs into dough one at a time, making sure to completely incorporate each egg before adding the next. Dough will look broken when eggs are added, but will come back together as you stir. The final texture should be smooth, glossy, and somewhat stretchy.

Step 3

Fit pastry bag with round tip. Spoon dough into bag. Holding bag at an angle so the tip is just touching prepared baking sheet on one side, gently start to squeeze out dough. Without moving the tip (this will help you make a perfect circle), pipe dough until you have a 1½" round (you can trace circles on the back of the parchment for extra accuracy). Repeat, staggering rounds and spacing 2" apart.

Step 4

Beat remaining egg in a small bowl until no streaks remain and lightly brush tops of dough. Bake 15 minutes, then lower heat to 350˚. Continue to bake until puffs are deep golden brown all over and sound hollow when tapped on the bottom, 10–15 minutes.

Step 5

Do Ahead: Dough can be made 1 day ahead; transfer to pastry bag and chill. Puffs can be baked 2 days ahead; store airtight at room temperature. Reheat at 350° for 5 minutes to crisp; puffs are easier to fill when firm.

Step 6

Place milk, butter, and salt in a medium saucepan, then scrape in vanilla seeds and add pod. Bring to a simmer over medium heat.

Step 7

Meanwhile, whisk egg yolks and granulated sugar in a medium bowl until very pale and light, about 3 minutes. Add cornstarch, whisking until no powdery dry spots remain. Whisking constantly, gradually add hot milk mixture to egg mixture. Transfer back to saucepan and cook over medium heat, whisking constantly, until mixture is thick and holds whisk marks, about 2 minutes.

Step 8

Strain custard through a fine-mesh sieve into a medium bowl. Cover with plastic, pressing directly onto surface; chill until cold, at least 2 hours.

Step 9

Fit pastry bag with star tip. Transfer chilled pastry cream to bag. Working one at a time, poke a hole into the bottom of each puff with a paring knife. Gently pipe in pastry cream to fill. Puffs will begin to get soggy as soon as they are filled, so wait until just before serving to add pastry cream.

Step 10

Do Ahead: Pastry cream can be made 3 days ahead. Transfer to pastry bag and chill.

Step 11

Line a rimmed baking sheet with parchment paper and trace an 8" circle on parchment; turn it over (the circle will still be visible; this is just a guide).

Step 12

Fill a large bowl with ice water. Bring sugar, corn syrup, and ½ cup water to a boil in a medium saucepan over medium-high heat, stirring to dissolve sugar. Boil, brushing down sides with a damp pastry brush and swirling pan occasionally (do not stir), until caramel turns a light amber color. Set bottom of saucepan in ice water to stop the cooking and firm caramel slightly (if caramel is too thin, it will be runny and drip too much).

Step 13

Carefully dip tops of filled puffs in caramel and place, caramel side up, on an unlined rimmed baking sheet; let sit until caramel is set. (If caramel becomes too hard before all puffs are dipped, reheat over medium-low to loosen.)

Step 14

Use the 12 largest puffs for the bottom layer of your croquembouche. Working quickly, dip the side of 1 puff into caramel (you want just enough caramel to allow you to “glue” puffs together) and stick hot caramel side down onto parchment just inside the 8" circle; the top of the puff should be facing out. Dip another puff in caramel on the side in two places (at 9 o’clock and 6 o’clock) and position on parchment so that 1 spot of hot caramel will adhere to the side of the first puff and the other spot is on the parchment (again, top of puff should be facing out). Using the circle as your guide, repeat with remaining 10 puffs to complete your bottom layer.

Step 15

Set out 11 puffs to make the second layer (you may not need all of them) and use caramel to stick them together the same way as the first layer, doing your best to anchor puffs in the spaces in between the bottom puffs (this will make the croquembouche more sturdy).

Step 16

Continue to build croquembouche, making slightly smaller circles for each layer and reheating caramel as needed. Finish tower with a single puff; you should have about 8 layers total.

Step 17

Once croquembouche is assembled, let caramel in pan cool until it just begins to form a thread when you lift it from the pot with a fork. (The cooler it gets, the faster it will harden until it hardens mid-air.) Dip fork in caramel and quickly circle over and around croquembouche, letting caramel fall where it may (puffs should be encased in airy strings of caramel when you are done). Let caramel cool to harden.

Step 18

Do Ahead: Croquembouche can be assembled 8 hours ahead. Chill until ready to serve.