Preheat the oven to 350 degrees. Heat the olive oil in a large cast iron skillet (or oven-proof skillet) over medium heat.
Add the onion, red bell pepper, and broccoli and sprinkle with 1/2 teaspoon of the salt. Cook and stir for 5 minutes, then reduce the heat to low and cover with a lid. Cook for 5 more minutes, or until the veggies are tender. Add the garlic and cook until fragrant, about 30 seconds.
Whisk the eggs with warm water. Add in the rest of the salt, black pepper, cheddar cheese, and 1/4 cup of the Parmesan cheese. Pour the egg mixture over the vegetables in the skillet.
Cook for about 5 minutes, or until the eggs begin to set along the pan's edge. Run a spatula around the edge to allow the uncooked eggs to run underneath. Cook for a couple more minutes and repeat this procedure.
Sprinkle the remaining Parmesan cheese, red bell pepper rings, and crushed red pepper flakes on top. Remove from the heat and place the frittata in the preheated oven. Bake for about 15 minutes, or until the eggs are set.
Place the frittata under the broiler for a couple of minutes to brown the top, if desired. Cut into wedges and serve.
To substitute frozen broccoli florets for the fresh broccoli, thaw first and drain off any liquid.Instead of broccoli, try making this frittata using zucchini, asparagus, or spinach.