Preheat your oven to 350°F (175°C).
In a large mixing bowl, whisk together the eggs, milk, salt, and black pepper until well combined.
Stir in the shredded cheese, diced bell peppers, and diced ham or bacon (if using).
Lightly grease the rimmed baking sheet with cooking spray or a little oil.
Pour the egg mixture into the prepared sheet pan and spread it out evenly.
Bake in the preheated oven for 20 minutes, or until the eggs are set and slightly golden on top.
Remove the pan from the oven and let it cool for a few minutes. Use a spatula to cut the baked eggs into squares.
While the eggs are cooling, toast the English muffins or bagels with butter or oil until golden brown.
Assemble each sandwich by placing a square of the baked eggs between the toasted halves of the English muffin or bagel.
Serve warm and enjoy!