How to Make It
Preheat the oven to 400°. Line 2 large baking sheets with parchment paper. In a medium saucepan, combine the 1/2 cup of water with the whole milk, butter, condensed milk and 1/4 teaspoon of salt and bring to a boil. Remove from the heat and add the flour all at once; stir with a wooden spoon until a smooth mass forms. Return the saucepan to the heat and cook over moderate heat, stirring constantly, until the dough pulls away from the sides of the pan and begins to dry out, 4 to 5 minutes.
Transfer the dough to a large bowl and beat at medium speed until cooled slightly, about 1 minute. At low speed, beat in the whole eggs, 1 at a time, beating until incorporated between additions. Beat in 1 of the egg yolks until incorporated.
Transfer the dough to a pastry bag fitted with a 1/2-inch plain tip. Pipe thirty 1 1/2-inch mounds onto the baking sheets, about 1 inch apart. In a bowl, mix the remaining egg yolk and 2 tablespoons of water. Lightly brush each mound with the egg wash and sprinkle lightly with sea salt. Bake for 10 minutes, until puffed and lightly browned. Lower the oven temperature to 350° and bake the puffs for 20 minutes longer, until golden and crisp. Let cool on the sheets, then slice each puff in half horizontally.
Line a baking sheet with wax paper. Working with 6 puffs at a time, fill each puff with the ice cream; replace the tops. Freeze the profiteroles on the baking sheet while you fill the rest. Freeze the filled profiteroles just until firm, about 20 minutes.
In a saucepan, combine the coffee, cocoa powder, sugar, corn syrup and 1/4 teaspoon of salt; whisk until smooth. Bring to a boil, whisking constantly. Remove from the heat and whisk in the chocolate, butter and coffee liqueur. Transfer the sauce to a pitcher.
Transfer the profiteroles to plates. Drizzle with the mocha sauce and serve.
After piping out all the profiterole dough, flatten any pointy tips that stick up with a wet finger. These small tips can burn before the puffs are fully baked. For even baking, switch the position of the sheets on the oven racks halfway through.