Filling: In large skillet, heat oil over medium heat; fry onion, zucchini and oregano, stirring occasionally, until tender, about 6 minutes. Stir in red pepper. Transfer to small bowl; set aside.
In bowl, whisk together eggs, salt, pepper and 2 tbsp (25 mL) water just until blended but not frothy.
In 8-inch (20 cm) nonstick skillet, melt 1 tsp (5 mL) of the butter over medium heat. Add one-quarter of the vegetable mixture and one-quarter of the egg mixture, making figure eight with spatula to combine. Sprinkle with cheese. Cook until almost set, gently lifting edge with spatula to allow any uncooked eggs to flow underneath, about 3 minutes.
Fold in half; cook for 2 minutes. Slide onto plate. Repeat with remaining ingredients.