Use this batter recipe for cream puffs as well as eclairs.
Preheat oven to 400 degrees. Line 2 baking sheets with parchment paper; set aside. Put butter, milk, sugar, salt, and 1/2 cup plus 2 tablespoons water into a medium saucepan. Bring to a boil, stirring until sugar has dissolved. Remove from heat. Add flour all at once, and stir until combined. Return to heat; cook, stirring constantly, until mixture pulls away from sides and a film forms on bottom of pan, about 1 minute more.
Transfer batter to the bowl of an electric mixer fitted with the paddle attachment, and mix on medium speed until cooled, about 5 minutes. Add 5 eggs, one at a time, mixing well after each addition. Mix until very smooth, about 1 minute.
Transfer batter to a pastry bag fitted with a 1/2-inch plain round piping tip (such as Ateco #806). Pipe a small amount of batter under each corner of parchment to hold it in place on sheet. For cream puffs, pipe 1 1/2-inch rounds (about 1 inch high) onto parchment, spacing about 2 inches apart. For eclairs, pipe 2-by-1-inch rectangles (about 1 inch high) onto parchment, spacing about 2 inches apart. Whisk remaining egg with 1 teaspoon water. Gently smooth tops with a moistened fingertip; lightly brush with egg wash.
Bake 15 minutes. Rotate sheets, and reduce oven temperature to 325 degrees. Bake until cooked through and dry in center, 20 to 25 minutes more. Transfer to wire racks set over parchment; let cool completely. Unfilled puffs and eclairs can be stored in an airtight container up to 3 days.
Cut puffs and eclairs in half horizontally. Dip tops in poured fondant. Return to wire racks, and let set.
Fill a pastry bag fitted with a 3/8-inch fluted tip (such as Ateco #864) with mousseline, and fill bottoms of puffs and eclairs. Sandwich with tops. Serve immediately.