Preheat the oven to 375°F (190°C).
Heat the extra virgin olive oil in a 10-inch oven-safe non-stick skillet over medium heat.
Add the diced bell peppers to the skillet and sauté for 4-5 minutes until they are tender and slightly caramelized.
In a medium bowl, whisk together the eggs, egg whites, sea salt, and black pepper until well combined and frothy.
Pour the egg mixture into the skillet over the sautéed peppers, ensuring they are evenly distributed.
Sprinkle the shredded sharp cheddar cheese and fresh chives over the top of the egg mixture.
Cook on the stovetop for 2-3 minutes without stirring, until the edges of the frittata begin to set and pull away from the sides.
Transfer the skillet to the preheated oven and bake for 10-12 minutes, or until the center is just set and the top is lightly golden.
Remove from the oven, let it rest for 2 minutes, then slice and serve.