In a saucepan, heat up the water, butter, sugar, and salt until the butter melts.
Add the flour all at once and stir vigorously until the water are all absorbed by the flour. Keep moving it around the pan until the dough comes together.
Transfer the dough into a stand mixer. Let cool for awhile. Mix in the eggs, one at a time, and mix thoroughly until the dough is smooth.
Put one baking tray on top of another. This helps the bottom of the choux from getting too brown. Line the baking tray with parchment paper. Sprinkle the parchment lightly with water.
Pipe the dough to a 2 inch mound on the parchment paper and space for about 2 inch apart. Dip your finger in a bowl filled with water and flatten the top of the mound with it.
Bake for about 25 minutes then turn it around and bake for another 5 minutes.
Remove from oven and prick with a toothpick and let cool.
Pastry Cream
In a saucepan, heat up the milk until it comes almost to a boil.
In a medium bowl, mix together the egg yolks, sugar and cornstarch.
When the milk is warmed up, gently pour it into the egg yolk mixture while whisking it slowly.
Pour all the mixture back into the saucepan. Keep stirring on medium high heat until the mixture thickens up. Be careful it might bubbles and splatter.
Add the butter and mix again. Add the rum and mix again. Transfer into a bowl. Put a plastic wrap right on top of the pastry cream so it doesn’t make a skin. Cool down.
Chill in the refrigerator for about 2 hours before using.
Using a small round piping tip, pipe the pastry cream into each choux pastry.
Caramel
Put the sugar and water in a saucepan. DO NOT STIR.
Bring it to a boil until it becomes a light golden caramel. Dip the bottom of the pan in an ice bath so it will stop the cooking.
Start assembling the tower of cream puffs by dipping the sides of the cream puffs and assemble it together using a cone foam.