Steam the broccoli until tender, then allow it to cool slightly.
Finely chop the cooled broccoli and transfer it to a medium or large bowl.
Add the cheese, red pepper flakes, some of the Panko breadcrumbs, and one beaten egg. Mix everything together thoroughly.
Scoop 1-2 tablespoons of the mixture and shape it into balls.
Refrigerate the balls for an hour to help them set.
Set up three separate bowls: one with flour, one with beaten eggs, and one with the remaining Panko breadcrumbs for coating.
Heat the oil to 375°F in a large skillet, using a thermometer to ensure the oil is at the right temperature.
Dredge each ball in the flour, then dip it in the egg, and finally coat it with Panko breadcrumbs.
Carefully place the coated balls in the hot oil and fry for a few minutes on each side, cooking in batches to ensure enough space between each ball.
Once the breading is golden brown on all sides, transfer the balls to a paper towel-lined tray to drain excess oil. Serve warm.