Shred the zucchini using a large eye grater, over a colander.
Squeeze out moisture from the mixture, using a clean kitchen towel, squeeze out as much liquid as you can.
Place squeezed zucchini in a medium bowl, beat egg slightly, and add to zucchini, goat cheese, mint, onion, cumin, salt, and pepper to taste.
Stir in the whole wheat flour.
Heat 1 Tbs oil in a sauce pan.
Drop 1/4 cup mounds of zucchini mixture into the hot oil, .repeating to make as many patties as will fit in the skillet, about 4 at a time.
Flatten them with the back of a spoon to form pancakes, and spread them about 1/2 inch apart, so they don't stick together, and are easy to turn over and cook until golden brown on both sides and cooked all the way through, 3 to 5 minutes per side.
Remove them onto a plate lined with a double layer of paper towel, to absorb any extra oil.