Preheat your oven to 350°F (175°C).
Brush a non-stick muffin tin with olive oil to prevent sticking.
In a large mixing bowl, whisk together the 6 whole eggs and the 6 egg whites until well combined.
Add the freshly grated parmesan and mozzarella cheese, kosher salt, and black pepper to the egg mixture. Mix until well incorporated.
Gently fold in the thin strips of red or orange bell pepper.
Pour the egg mixture evenly into the prepared muffin tin, filling each cup about 3/4 full.
Bake for 20-25 minutes, or until the quiches are set and lightly golden on top.
Remove from the oven and allow to cool in the tin for about 5 minutes, then transfer to a serving platter.