Whisk together eggs, salt and pepper. In non‐stick skillet, heat oil over medium‐low heat; pour in egg mixture. Cook, stirring constantly, until eggs are creamy and softly set, approximately 5 minutes.
Toss together avocado, lime juice, and pinch each of the salt and pepper. Layer lettuce, avocado, cucumber, scrambled eggs and sprouts over bottom halves of English muffins. Cap with top halves of muffins.