Heat the oil in a large skillet over medium heat. Add the onions and garlic and cook, stirring occasionally, until they begin to soften. Add the broccoli and give everything a stir. Cook until the broccoli just begins to soften, about three minutes. Remove from the heat.
In a large bowl, whisk the eggs, then whisk in the panko, cheddar and Parmesan. Add the broccoli mixture and stir to combine thoroughly. Use your hands to form six patties. Don’t worry about making them perfectly round, but do try to make them even in thickness. Arrange the patties on the baking sheet.
Bake for 15 minutes. Use a spatula to flip the patties, then bake for another ten minutes. Allow the patties to cool on the baking sheet and then store in an airtight container. They’ll keep for three or four days in the fridge and up to three months in the freezer.
Recipe excerpted from The School Year Survival Cookbook.