Steam or microwave the chopped broccoli until tender, then drain and chop finely.
In a mixing bowl, combine the broccoli, cheddar cheese, 1/2 cup breadcrumbs, parmesan, 1 beaten egg, garlic, salt, and pepper.
Shape the mixture into small balls using your hands.
Roll each ball in flour, dip into the beaten eggs, and then coat with breadcrumbs.
Heat oil in a deep pan over medium-high heat.
Fry the broccoli balls in batches until golden brown and crispy, about 3-4 minutes per batch.
Drain on paper towels and serve warm with your favorite dipping sauce.