In a large sauté pan, heat 1 tablespoon olive oil on medium heat.
Add broccoli, salt and pepper, and stir. Cook until broccoli is bright green, about 2-3 minutes.
Add asparagus and garlic. Cook, stirring often to prevent burning, until vegetables are tender, about 4-5 minutes. Reduce heat to medium-low if needed. Remove from heat, place cooked vegetables in a bowl, and set aside.
Starting with a clean sauté pan, heat remaining olive oil on medium heat, tilting pan to evenly coat. Once oil is hot, but not smoking, add eggs.
As eggs cook, use a rubber spatula to push the edges of the egg mixture toward center of pan, allowing uncooked eggs to flow underneath and make contact with the pan. Repeat procedure until all eggs are set.
When eggs are set, but still shiny, top with vegetable mixture and shredded cheese. Remove from heat, fold omelet in half and slide onto a plate to serve.
Optional: cook eggs in 2 batches if using a medium sauté pan.