Steam broccoli florets until tender but still bright green. Let cool slightly, then finely chop.
In a large bowl, combine the chopped broccoli, cheddar cheese, mozzarella cheese, breadcrumbs, Parmesan, eggs, flour, garlic powder, onion powder, salt, and pepper. Mix until fully combined.
Scoop about 1 tablespoon of the mixture and roll it into a ball. Repeat until all the mixture is used.
Roll each ball in additional breadcrumbs to coat.
To Fry:
Heat oil in a deep skillet or fryer to 350°F (175°C). Fry balls in batches for about 2–3 minutes, until golden and crispy. Drain on paper towels.
To Bake:
Preheat oven to 400°F (200°C). Place balls on a greased baking sheet, lightly spray with oil, and bake for 12–15 minutes until golden, flipping halfway through.
Serve warm with your favorite dipping sauce like ranch, marinara, or a spicy aioli.