In a mixing bowl, crack the three large eggs and add the 1/4 cup of milk. Whisk until well combined. Add salt, black pepper, and garlic powder, and whisk again until blended smoothly.
Fold in the 1/4 cup of shredded cheese, diced bell peppers, and diced onions into the egg mixture until evenly distributed.
Preheat your waffle iron and lightly grease it with 1 tablespoon of olive oil. Pour half of the egg mixture into the waffle iron and cook for about 4-5 minutes until set and lightly browned. Repeat with the remaining mixture.
In a small saucepan, combine 1 cup of shredded cheese, 1/2 cup of heavy cream, 1/4 teaspoon of paprika, and 1/4 teaspoon of salt. Heat over medium, stirring continuously until the cheese melts and the sauce is smooth.
Place one waffle omelet on a plate and drizzle with the warm cheese sauce. Add any extra toppings if desired and serve hot.