Dump grated zucchini in a colander placed in the sink or over paper towels. Sprinkle over salt. Let sit for 10 to 15 minutes to draw out the moisture. Transfer zucchini to 2 layers of paper towels. Wrap towels around the zucchini and press out as much moisture as possible.
Add zucchini, garlic, flour, cheeses, egg, and spices to a large bowl and mix until combined.
Heat a pan over medium high heat. Pour in half of the oil. Form zucchini mixture into golf ball sized balls or spoon directly into the pan. Press flat with the back of a spatula.
Cook for about 2 minutes, until browned and then flip to the other side. Cook for another 2 minutes. Repeat with remaining batter.
Transfer to a place lined with a paper towel. Keep warm in a warm oven (less than 200 degrees), until ready to serve.