Bring a medium-sized pot of salted water to a boil. Add the broccoli florets and cook them just until they are fork-tender, about 5 minutes. Using a large, sharp knife, cut them into very small pieces.
In a medium-sized bowl, combine the chopped broccoli, eggs, Parmesan, flour, and garlic. Season with salt and pepper to taste. Stir until well combined.
Place a cast iron or non-stick pan over medium heat until hot. Add the oil and swirl to coat the pan. Scoop out 2- to 3-tablespoon mounds of the broccoli mixture into the pan, flattening the mounds slightly.