Crack eggs directly into medium bowl. Add milk of choice, then whisk ingredients together vigorously until mixture is pale and foamy, with no streaks of yolks or egg whites remaining. Set egg mixture aside.
Heat medium skillet over medium heat. When pan is hot, add olive oil and swirl pan to coat. Heat skillet until oil is hot and shimmery, then add onion, bell pepper, and tomato. Sauté 3 minutes or until vegetables are tender, then transfer vegetables to small bowl.
Carefully and quickly wipe skillet out with paper towels. Add more oil if needed, then pour egg mixture into center of hot skillet. Use spatula to spread egg mixture out to edges of skillet, then cook eggs, undisturbed, until almost fully set, approximately 2 to 3 minutes.
Spread sautéed vegetables evenly over top of omelette, then sprinkle shredded cheese over. Let omelette cook, undisturbed, 1 to 2 minutes or until cheese has melted.
Remove skillet from heat. Carefully slide spatula under one edge of omelette, then gently fold lifted edge to meet opposite side of omelette, folding omelette in half. Slide folded omelette out of skillet and onto plate.
Top omelette with sour cream, salsa or pico de gallo, chopped cilantro, slices of avocado, or jalapeño as desired. Serve immediately.