In a colander set over a bowl, place the shredded zucchini and sprinkle with salt. Let stand for 10 minutes.
Place zucchini in a clean tea towel and squeeze liquid out of zucchini. Squeeze out as much liquid as possible. Transfer to a large bowl.
Stir in the flour,Panko bread crumbs, Parmesan cheese eggs, sliced green onions, salt, and pepper to the zucchini. Line a plate with paper towels.
In a large skillet over medium heat, heat the olive oil. Scoop about a 1/4 cup mounds of the zucchini mixture into the pan, pressing them into rounds. Cook for 2 to 3 minutes, then flip them once and cook an additional 2 minutes until golden brown.
Transfer the zucchini fritters to the paper towel-lined plate and immediately sprinkle them with salt.
Repeat until the mixture is gone. Serve the zucchini fritters and top with sour cream (optional).