Heat the extra virgin olive oil in a medium non-stick skillet over medium heat.
Add the diced bell peppers to the skillet and sauté for 3-4 minutes until they are tender-crisp and slightly caramelized.
In a medium mixing bowl, whisk together the whole eggs, liquid egg whites, sea salt, and black pepper until the mixture is uniform and slightly frothy.
Pour the egg mixture into the skillet over the peppers, tilting the pan to ensure the eggs cover the entire surface.
Let the eggs cook undisturbed for about 1 minute, then use a silicone spatula to gently lift the edges, allowing the raw egg to flow underneath.
Once the eggs are mostly set but still slightly moist on top, sprinkle the shredded sharp cheddar cheese over one half of the omelette.
Carefully fold the other half of the omelette over the cheese and cook for another 60 seconds until the cheese is fully melted.
Slide the omelette onto a plate, garnish with freshly minced chives, and serve immediately.