- Whisk ½ cup mayonnaise, 2 teaspoons lemon juice, 1 minced garlic clove, 1 teaspoon smoked paprika, and ⅛ teaspoon cayenne pepper together in small bowl. Season with table salt to taste; set aside.
- Combine 1 finely chopped onion, ½ cup water, 1 tablespoon extra-virgin olive oil, and ¼ teaspoon salt in 10-inch nonstick skillet. Cover and cook over medium heat, stirring occasionally, until water has evaporated and onions are tender but not browned, about 10 minutes. Transfer onions to large bowl and wipe out skillet with paper towel.
- Add 10 eggs, ¼ teaspoon pepper, and remaining ½ teaspoon salt to bowl with onions and whisk until eggs are thoroughly combined and color is pure yellow. Fold in 6 ounces plain kettle-style potato chips with spatula until well coated. Let sit, stirring occasionally, until chips soften and wilt (some will break; that’s OK), about 5 minutes.
- Heat 3 tablespoons oil in now-empty skillet over medium-high heat for 1 minute. After 1 minute, test heat of skillet by spooning small amount of egg mixture into center or pan. If it sizzles and puffs immediately, skillet is properly heated (if not, wait until it puffs before adding remaining egg mixture). Pour in egg mixture and cook, gently shaking pan while stirring and dragging eggs across skillet with spatula for 20 seconds. Neaten eggs around perimeter and smooth top with spatula. Cover; reduce heat to medium; and cook, gently shaking and rotating pan occasionally, until bottom of tortilla is set and golden brown, 2 to 2½ minutes (not all of egg on top will be fully set).
- Remove skillet from heat and uncover. Using spatula, loosen tortilla from pan, shaking back and forth until tortilla slides around freely. Slide tortilla onto large plate. Cover with second plate and flip to invert tortilla. Add remaining 1 tablespoon oil to skillet and slide tortilla, browned side up, back into skillet. Tuck edges of tortilla into skillet with spatula. Return heat to medium and continue to cook, uncovered, gently shaking and rotating pan every 30 seconds, until second side is golden brown and center of tortilla registers 150 to 155 degrees, about 2 minutes longer.
- Slide tortilla onto cutting board or serving platter and let cool for at least 5 minutes. (For more rounded sides, invert platter or cutting board over skillet. Using pot holders, swiftly and carefully invert tortilla onto platter.) Cut tortilla into wedges or cubes, sprinkle with 2 tablespoons chopped chives, and serve with allioli.
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