The ice cream transforms this French pastry into a delectable ice cream sandwich.
Preheat oven to 425 degrees with a rack in the center. Line two unrimmed baking sheets with parchment paper or Silpats (French nonstick baking mats).
Make Pate a Choux batter. Fill a pastry bag fitted with a coupler or 1/2-inch (Ateco No. 806) tip, and pipe 2-inch rounds that are about 1 inch high onto baking sheets at 2-inch intervals.
Using your finger, gently rub egg wash over entire top, and flatten the tips, being careful not to let it drip down onto sheet (it will inhibit rising). Cover one sheet with lightly oiled plastic wrap, and place in refrigerator. Transfer the other to the oven. Bake for 10 minutes; reduce oven heat to 350 degrees. Bake until puffs are golden brown, 15 to 20 minutes more. Turn off oven, and prop door open slightly to let steam escape. Allow profiteroles to dry out in the oven about 15 minutes, or until the center is slightly damp but no wet dough remains (test by cutting into the center of one). Transfer to a wire rack to cool completely. Raise heat back to 425 degrees, and repeat process for remaining batch.
Scoop out 26 balls of ice cream, and place on parchment-lined baking sheet. Place in freezer to reset for 20 minutes.
To make chocolate sauce, place chocolate in a bowl. Combine cream and corn syrup in a small saucepan; bring to a boil. Pour over chocolate; let sit 5 minutes, and stir to combine. Allow it to cool slightly before serving, or store in refrigerator up to 1 week and gently reheat over low heat before serving.
Cut each profiterole in half horizontally, and fill with a scoop of ice cream. Place two profiteroles on each plate, and top with warm chocolate sauce.
Garnish with delicate curls made by shaving chocolate with a vegetable peeler.