Prepare one or two plates by covering them with paper towels and having them ready for when the fritters are done.
Grate zucchini on the large holes of a box grater or using the grating blade of a food processor. Place grated zucchini in a strainer over a large bowl, and gently toss with 1/4 tsp coarse salt. Let rest for 5 minutes.
Meanwhile, grate the onion (use the same thing as the zucchini so they are the same size). Gently mix the grated onion into the zucchini. Let sit for another 5 minutes.
Squeeze zucchini-onion mixture dry. Use your hands, in a clean kitchen towel, or press in a ricer. (liquid can be discarded or added to your next batch of stock)
Mix together zucchini, onion, cheese, flour, and herbs. Season with 1 tsp salt and 1/4 tsp pepper.
Stir the eggs into the zucchini mixture just before frying.
Heat a medium skillet over medium-high heat.
Working in batches, coat skillet with 1-2 Tbsp oil. Scoop mounds (2 Tbsp each) of the mixture into skillet; flatten slightly using a spatula. Cook until golden brown and cooked through, 2-3 minutes per side.
Transfer fritters to paper-towel-lined plates to drain. Serve with sour cream and applesauce.