Preheat the oven to 375°F (190°C).
Lightly oil a 12-cup mini muffin tin or a 6-cup regular muffin tin using cooking spray or a thin layer of oil.
In a mixing bowl, whisk the 6 large eggs until combined and slightly frothy.
Add the diced red bell pepper, diced zucchini, finely diced onion, grated cheddar, salt, and black pepper to the eggs and stir until evenly distributed.
Pour the egg mixture into the prepared muffin cups, filling each about three-quarters full.
Bake for 15–20 minutes, until the egg muffins are set and lightly golden on top.
Let the muffins cool slightly before removing them from the tin.