On medium-high heat bring the water, butter, sugar, and salt to a simmer. When the butter has completely melted, add the flour and mix vigorously with a wooden spoon. With every bit of elbow grease you can muster, continue mixing for 4 minutes. A mass of dough will form and it will begin to come away from the sides and bottom of the pot. Remove from the heat and transfer dough to a stand mixer outfitted with a paddle attachment. Add eggs one at a time, making sure each is consumed by the dough before you add the next. You can also leave it in the pot and mix by hand.
Cool for a couple of minutes, stirring occasionally to release steam. When cool enough to handle, transfer into a piping bag. Pipe out 1-inch rounds. Smooth out any pointy peaks by dipping your finger in water and gently pressing them out; this will ensure an even bake. Bake until golden brown, approximately 20 minutes. Allow them to cool then fill them with pastry cream.
For the pastry cream: In a small heavy-bottomed pot, warm the milk gently to a simmer. If you want to flavor your pastry cream, do so now: You can use vanilla, lavender, or even a chai tea bag. Allow a half hour for the flavors to mature, and then reheat back to a simmer.
Meanwhile, mix the sugar, salt, yolks, and cornstarch together in a bowl. Temper by adding half of the hot milk into eggs, whisking feverishly. Add the egg mixture back to the milk and stir constantly with a wooden spoon on medium high heat until it coats the back of the spoon. Immediately transfer to a bowl and stir a couple minutes to cool down, then add the butter and mix well. Place a piece of plastic wrap directly on the cream so as not to create a skin. Chill until completely cooled.
Transfer to a piping bag, poke each cream puff gently with the tip of the bag, and fill.
For caramel, place 2 cups of sugar and 1/4 cup of water in a pan, stir to combine, and cover. Cook over medium-high for about 15 minutes, until the caramel is a light amber.
With tongs, gently dip each cream puff into the caramel and begin to start stacking your croquembouche. Make sure your base is sturdy and continue upwards.
Once you are done mounting reheat, your caramel until it turns a darker shade of amber. Allow to cool for a few minutes until it resembles the constituency of honey, then with a spoon drizzle it about, try to get thin stings of the caramel to wrap around. I also drizzled some ganache over everything and dusted it with powdered sugar.
Eat within 2 to 3 hours, as the caramel will start to soften.