In a large saucepan over medium heat, add butter, water, sugar and salt, and bring to a boil. Once it begins to boil, remove from heat. Add the flour and stir with a wooden spoon. Return to the heat for 30 seconds and continue stirring. 

Transfer to a bowl of a stand mixer fitted with the paddle attachment. Over medium speed, add one egg at a time, stopping to scrape down the sides. Mix until fully combined. The dough should be glossy and thick. Transfer dough to a pastry bag fitted with a standard round tip. 

Pipe the dough onto a parchment paper lined baking sheet. Pipe 1.5" circles and tap the tops with water to remove any peaks. Brush the surface with an egg wash.

Bake for 15 minutes. Do not open the oven door! Allow to cool on baking sheet. 

Add the milk and vanilla extract to a saucepan over medium heat and bring to a boil. Remove from heat and let cool for 10 minutes.

In a bowl of a stand mixer fitted with the paddle attachment, beat the egg yolks and sugar until pale yellow and fluffy. Sift the flour and add to the egg mixture. Beat until combined.

Add half of the milk into the batter and mix. Add remaining milk and beat until fully combined.

Transfer the mixture back into the saucepan. Cook over medium heat, whisking constantly for 8-10 minutes until custard begins to thicken. Add the butter and whisk until melted and fully combined.

Strain the custard into a bowl and allow to cool for 15 min. Cover with plastic wrap, pressing against the surface to prevent a film from forming at the top. 

Chill for at least 2 hours. You can also make it a day ahead. 

Poke a hole into the bottom of the puff and gently fill it with custard.

Bring sugar, corn syrup and water to a boil. Cook over medium heat until sugar dissolves and turns light amber, about 20 minutes. Remove from heat.

Dip the tops of the cream puffs into the caramel and place them on a lined baking sheet. Let cool for 30 minutes. Dip the bottom and sides of puffs into caramel and begin assembling your tower. 

Form the base by arranging 12 cream puffs in a large circle, tops facing out. 

Continue this process working your way up. The caramel will act as the glue sticking them together. 

When it’s finished, drizzle with caramel or decorate with spun sugar. You can stick elements such as Christmas ornaments.