Instructions

1. Adjust oven rack to middle position and heat oven to 425 degrees. Spray large (12-by 18-inch) baking sheet with nonstick cooking spray and line with parchment paper; set aside. Beat eggs and egg white in measuring cup or small bowl; you should have 1/2 cup (discard excess). Set aside.
2. Bring butter, milk, water, sugar, and salt to boil in small saucepan over medium heat, stirring once or twice. When mixture reaches full boil (butter should be fully melted), immediately remove saucepan from heat and stir in flour with heatproof spatula or wooden spoon until combined and mixture clears sides of pan. Return saucepan to low heat and cook, stirring constantly, using smearing motion, for 3 minutes, until mixture is slightly shiny with wet-sand appearance and tiny beads of fat appear on bottom of saucepan (temperature of paste should register 175 to 180 degrees on instant-read thermometer).
3. Immediately transfer mixture to food processor and process with feed tube open for 10 seconds to cool slightly. With machine running, gradually add eggs in steady stream. When all eggs have been added, scrape down sides of bowl, then process for 30 seconds until smooth, thick, sticky paste forms. (If not using immediately, transfer paste to medium bowl, cover surface flush with sheet of plastic wrap sprayed lightly with nonstick cooking spray, and store at room temperature for up to 2 hours.)
4. Fold down top 3 or 4 inches of 14- or 16-inch pastry bag fitted with 1/2-inch plain tip to form a cuff. Hold bag open with one hand in cuff and fill bag with paste. Unfold cuff, lay bag on work surface, and, using hands or spatula, push paste into lower portion of pastry bag. Twist top of bag and pipe paste into 1 1/4- to 1 1/2-inch mounds on prepared baking sheet, spacing them about 1 to 1 1/4 inches apart (you should be able to fit about 24 mounds on baking sheet).
5. Using a wet finger, gently push down the tips of the dough until you are left with smooth, round mounds. Bake 15 minutes (do not open oven door), then reduce oven temperature to 375 degrees and continue to bake until golden brown and fairly firm (puffs should not be soft and squishy), 8 to 10 minutes longer. Remove baking sheet from oven. With paring knife, cut 3/4-inch slit into side of each puff to release steam; return puffs to oven, turn off oven, and prop oven door open with handle of wooden spoon. Dry puffs in turned-off oven until centers are just moist (not wet) and puffs are crisp, about 45 minutes. Transfer puffs to wire rack to cool.
6. Cooled puffs can be stored at room temperature for up to 24 hours or frozen in zipper-lock plastic bag for up to 1 month. (If storing at room temperature, leave on the wire rack and cover with a clean, completely dry dish towel for best results.) Before serving, crisp room temperature puffs in 300-degree oven 5 to 8 minutes, or 8 to 10 minutes for frozen puffs.