Preheat oven to 425 degrees and line a large baking sheet with parchment paper.
Pastry:
In a medium pot, over medium heat, add butter, sugar, and water. Bring it to boil, while stirring slowly, and take off heat. Stir in flour with a wooden spoon until all combined and coming off the walls of the pot easily.
Start whisking in eggs one at a time, making sure that each egg is mixed into the batter before adding the next.
Transfer batter into a piping bag and pipe little round mounts, about 1½-2 inches in size.
Whisk the 4th egg in a separate little mixing bowl and brush pastries with it before baking.
Bake pastries at 425 for 13-15 minutes then lower the heat to 350 and bake for another 10-12 minutes, until golden brown.
Let pastries cool completely before adding the filling.
Bailey's Whipped Cream:
Add the cold heavy whipping cream into the cold mixing bowl. Starting at low speed, start whisking, gradually raise to speed to high. Slowly pour in the sugar and then Baileys. Beat until stiff peaks appear (don't walk away far). Keep in the refrigerator until ready to use.
Transfer whipped cream into a piping bag.
Cut cooled pastries in the middle and fill them with whipped cream.
Chocolate:
Heat up hot fudge topping and whisk it with Bailey's until completely combined. Cool before using so it doesn't melt the whipped cream.
Once cooled, drizzle filled cream puffs with chocolate sauce.
**Note: I recommend preparing whipped cream and chocolate sauce while pastries are cooling so that sauce is cooled.**