1. Separate white and green parts of green onions. Set green parts aside. Cut whites into chunks. Add whites to food processor along with red pepper and cucumber. Pulse with on-and-off motion until finely chopped.
2. Whisk together oil, vinegar, salt, red-pepper seasoning if using, and black pepper in bowl. Add chopped vegetables from processor to oil mixture along with tomatoes; stir gently to combine. Refrigerate, covered, 1 hour, stirring occasionally.
3. Arrange lettuce leaves on individual salad plates. Spoon vegetable mixture over leaves. Or tear leaves into bite-size pieces. Add vegetable mixture; toss gently to combine. Coarsely chop reserved green part of green onion; garnish salad. Serve salad cold.