Steam the broccoli florets for about 4-5 minutes until tender but still crisp. Drain any excess water and chop the steamed broccoli into small pieces.
In a large mixing bowl, combine the chopped broccoli, shredded cheddar cheese, shredded mozzarella cheese, all-purpose flour, beaten eggs, dried oregano, paprika, salt, and black pepper. Mix until all ingredients are well combined.
Heat a non-stick skillet or frying pan over medium heat and lightly grease it with cooking spray or a small amount of oil.
Spoon the broccoli mixture into the skillet, forming small patties with about 1/4 cup of the mixture for each fritter. Flatten them slightly with a spatula.
Cook the fritters for about 3-4 minutes on each side, or until they are golden brown and crispy.
Once cooked, remove the fritters from the skillet and place them on a plate lined with paper towels to drain any excess oil.
Serve the broccoli fritters warm as a delicious appetizer or side dish. Enjoy them as they are or with your favorite dipping sauce.