The name for these cream puffs, profiteroles, is old French for "small gifts"; serving them today still makes everyone feel special.
Make the dough: Preheat oven to 425 degrees. with racks in upper and lower thirds. Butter two large rimmed baking sheets.
Combine butter, 1 cup water, and salt in a 2-quart heavy saucepan; bring to a boil over high heat, stirring until butter melts. Reduce heat to medium.
Add flour; cook, stirring with a wooden spoon, until mixture pulls away from the sides of the pan and forms a ball, 30 seconds to 1 minute (see Cook's Note). Remove from heat; cool 1 minute.
With an electric handheld mixer, beat in eggs, a little bit at a time, until completely incorporated (dough should look shiny and be soft enough to slowly fall off a spoon).
Bake the puffs: Drop heaping tablespoons of batter onto baking sheets (you should have 24 to 28), about 2 inches apart. Using a pastry brush, lightly brush puffs with egg wash (do not let it drip on sheets).
Bake, rotating sheets between racks halfway through, until puffed and brown, about 25 minutes. Remove from oven; turn oven off.
With a toothpick, poke a hole in each puff. Return to oven (still off) for 10 minutes (this helps puffs dry out).
Fill the puffs: When cool, halve each puff horizontally with a serrated knife.
Working in batches (to prevent ice cream from melting), place a small scoop of ice cream (2 to 3 tablespoons) in each bottom half. Replace tops; press gently. Arrange on one rimmed baking sheet; freeze until firm. Cover with plastic wrap; freeze up to 2 days.
Arrange 3 filled puffs in each of eight shallow bowls; drizzle with warm Hot Fudge Sauce. Serve immediately.
The dough is of the right consistency when it pulls away from the sides of the pan and looks like dry mashed potatoes.