1 cup water
Vegetable oil (for deep-frying)
1. In a medium saucepan, bring water butter and salt to a boil. Add 1 cup flour; stir over medium heat until mixture pulls away from edges of pan, about 1 minute. Transfer to medium bowl. Using a wooden spoon (or spatula), fold mixture for about 3 minutes. You’re doing this to cool the dough a bit before adding the eggs. Add eggs 1 at a time, beating well between additions. The mixture will look wet and mushy, but keep folding the egg mixture into the dough–it’ll eventually combine. Measure 1 1/4 cups dough and reserve (discard any remaining dough).
2. Place potatoes in medium saucepan. Add enough water to cover by 1 inch. Boil until tender, about 12 minutes. Drain. Press potatoes through ricer or food mill into large bowl. Add 1 1/4 cups reserved dough, salt, and white pepper. Fold dough into potatoes until completely combined, being sure to not overly mix which will make the potatoes gummy.
3. Line baking sheet with parchment paper. Transfer dough to ziploc bag, working the dough fitted with 3/4-inch-diameter plain tip. Pipe dough in logs onto prepared sheet. Freeze until firm but not frozen, about 1 hour. Cut logs into 1 inch-long pieces. Toss in flour, return to sheet, cover, and freeze completely. DO AHEAD Can be made 1 week ahead. Store in airtight container; keep frozen.
4. Pour enough oil into large saucepan to measure depth of 2 inches. Heat oil to 350°F. Working in batches, cook frozen potato pieces until cooked through and golden brown, stirring occasionally, about 3 minutes. Transfer to paper towels to drain. Sprinkle with salt and serve.