Sprinkle over 1 tablespoon Parmesan cheese and season with salt and pepper. Mix thoroughly.
Divide the zucchini mixture into four portions, shaping each into a round fritter in the skillet. Create a small well in the center of each fritter, and crack an egg into each well.
Cover the skillet with a lid and cook for about 5 minutes, or until the egg whites are set and the yolks are still runny.
Remove from heat, season with salt and pepper, and sprinkle over the remaining Parmesan. Serve immediately.