Preheat oven to 400°F (200°C) and line baking sheets with parchment paper.

Combine 1 cup water, 1/2 cup butter, and 1/4 teaspoon salt in a saucepan and bring to a rolling boil over medium-high heat.

Remove from heat and stir in 1 cup flour until a thick paste forms; return to low heat for 1 minute, stirring to dry slightly.

Transfer paste to a mixing bowl and let cool for 2 minutes; beat in 4 eggs one at a time, stirring vigorously until smooth and glossy.

Pipe walnut-sized mounds onto prepared sheets, spacing 2 inches apart, and smooth peaks with a wet fingertip.

Bake puffs for 25–30 minutes until deep golden brown and crisp; do not open oven the first 20 minutes to prevent collapse.

Cool puffs on a rack to room temperature; poke a small hole in the bottom of each to prepare for filling.

Heat 1 cup milk with vanilla bean seeds and pod over medium until steaming; remove from heat and infuse for 5 minutes.

Whisk 4 yolks, 1/4 cup sugar, 2 tablespoons cornstarch, and 2 tablespoons flour in a bowl until pale.

Temper yolk mixture by whisking in one-third of hot milk, then return to saucepan with remaining milk and cook over medium, whisking until thick at 170°F (about 2 minutes).

Remove from heat, stir in 2 tablespoons butter, strain into a bowl, cover surface with plastic wrap, and chill at least 30 minutes.

Fill a piping bag with chilled pastry cream and pipe into the bottom of each puff until just filled without leaking.

In a clean saucepan, combine 2 cups sugar, 1/2 cup water, and cream of tartar; heat over medium-high without stirring until syrup reaches 350°F on thermometer.

Remove from heat, stir in 2 tablespoons butter, and keep warm over a bowl of warm water to maintain dipping consistency.

Dip base of each filled puff into caramel and assemble on a cone mold in concentric rings from bottom up, using caramel as glue.

Allow tower to set, dust with powdered sugar, and decorate with spun sugar if desired before serving.