Preheat your oven to 350°F (175°C) and grease a 12-cup muffin tin with cooking spray.
In a large mixing bowl, whisk together the eggs, milk, salt, black pepper, and paprika until well combined. This forms the base for your omelet egg muffins.
Dice the bell peppers, onions, tomatoes, and any optional ingredients like ham or bacon.
Distribute the diced vegetables and optional ingredients evenly among the greased muffin cups.
Carefully pour the egg mixture over the fillings in each muffin cup, filling them about ⅔ of the way full.
Sprinkle shredded cheddar cheese on top of each muffin cup.
Place the muffin tin in the preheated oven and bake for approximately 15-20 minutes or until the omelet egg muffins are set and slightly golden on top. You can check for doneness by inserting a toothpick into the center of a muffin – it should come out clean when they are ready.
Allow the muffins to cool in the tin for a few minutes before using a butter knife to gently loosen the edges and remove them. Serve warm, and enjoy!