Grate the zucchini and add salt. Wait five minutes, then wrap the zucchini with cheesecloth or paper towels and squeeze out excess moisture.
Add drained zucchini to a large bowl and combine with carrot, egg, onion, and pepper. Stir in whole wheat flour and fold in feta cheese until it is evenly distributed.
Coat a cast iron frying pan with olive oil or nonstick spray. Divide the mixture into five patties (or 10 small “sliders,” if preferred). Cook over medium heat for 4-5 minutes per side, until golden brown. Serve on your favorite buns with any condiments you like.