Shred the zucchini using the largest holes on a cheese grater (or a food processor with a shredding disk).
Use a clean kitchen towel to squeeze out as much liquid from the zucchini as you can (discard the liquid).
Transfer to a large bowl and stir in the eggs, feta, mint, onion, cumin, salt, and pepper to taste.
Stir in the flour.
In a large nonstick skillet, heat 1 teaspoon olive oil over medium-low heat.
Scoop out the zucchini mixture using a ¼-cup measure and drop it into the pan, repeating to make as many patties as will fit in the skillet, about 4 at a time.
Gently flatten the patties with the back of the measuring cup and cook until golden brown on both sides and cooked all the way through, 3 to 5 minutes per side.