In an 8" skillet, heat olive oil over medium-low heat. Dice onion, pepper, and zucchini into small pieces. Add onion to skillet, cooking for 3-4 minutes then add zucchini and pepper. Stir and cook for another 3-4 minutes, until zucchini is tender. Remove from skillet and set aside.
Melt 1/2 tablespoon butter in the 8" skillet, swirling until the bottom of the pan is covered. Whisk together 2 eggs,2 tablespoons milk, 1/4 teaspoon black pepper, and 1/8 teaspoon sea salt until eggs are slightly frothy. Pour into the hot skillet. As the bottom of the eggs set, lift up the side of the eggs with a spatula and let uncooked eggs run under the cooked eggs. Continue until egg is fairly well set. Carefully flip the omelette over and sprinkle 1 ounce cheese, half the tomato, and half the veggies on one side. Fold over and remove from pan. Repeat with remaining eggs.