Preheat your oven to 350°F (175°C). This will ensure that your muffins bake evenly.
Grease your muffin tin with a little olive oil or use silicone muffin liners to prevent sticking.
In a skillet over medium heat, add 1 tablespoon of olive oil. Once hot, add the finely chopped shallot and red bell pepper. Sauté for about 3-4 minutes, or until softened. Season with a pinch of salt and pepper.
In a large mixing bowl, crack in the 10 eggs. Use a whisk to beat them until the yolks and whites are fully combined. Season the eggs with salt and pepper to taste.
Add the sautéed vegetables to the egg mixture and stir until well combined.
Evenly distribute the egg and vegetable mixture into the prepared muffin tin, filling each cup about 2/3 full.
Place the muffin tin in the preheated oven and bake for 18-20 minutes, or until the egg muffins are set and lightly golden on top.
Once baked, remove the muffins from the oven and allow them to cool in the tin for a few minutes. Then gently remove them and let them cool on a wire rack.