Adapted/copied from Smitten Kitchen, which I found after a hasty Google search.

Prepare your broccoli

Separate the florets from the stem(s). Cut the florets into 1-inch chunks. You should have about 3 cups of chopped broccoli total.

Steam the broccoli

Steam your broccoli until tender but not mushy: Use whatever method you prefer. My quickie, lazy method is to bring a 1/2-inch or so of water to a boil in a small saucepan, then add the broccoli, place a lid on it and simmer it for 5 to 6 minutes. Drain the broccoli, then set it aside to cool slightly.

Preparing the "batter"

In the bottom of a large bowl, lightly beat your egg. Add the flour, cheese, garlic, salt and pepper. Then, add the somewhat cooled broccoli and, using a potato masher, mash the broccoli just a bit. You’re looking to keep the bits recognizable, but small enough (1/4- to 1/2-inch chunks) that you can press a mound of the batter into a fritter in the pan. Once mashed a bit, stir or fold the ingredients together the rest of the way with a spoon. Adjust seasonings to taste.

Frittering the fritters

Heat a large, heavy skillet over moderate heat. Once hot, add a good slick of oil (I usually use a mix of olive and vegetable oil), about 2 to 3 tablespoons. Scoop a two tablespoon-size mound of the batter and drop it into the pan, then flatten it slightly with your spoon or spatula. Repeat with additional batter, leaving a couple inches between each. Once brown underneath, about 2 to 3 minutes, flip each fritter and cook on the other side until equally golden, about another 1 to 2 minutes.

Transfer briefly to paper towels to drain, then to a serving plate if you’ll be eating them shortly or a baking sheet in a 200 degree oven if you’d like to keep them warm for a while until needed. Repeat with remaining batter, adding more oil as needed. Serve with some of the suggestions listed in the head notes, above.