Grate zucchini using a large cheese grater. Place in a colander over the sink or large bowl. Sprinkle with salt and toss to combine. Let sit for 5-10 minutes, or until most of the liquid has drained from the zucchini. Use your hands to squeeze out the remaining liquid.
In a bowl, combine zucchini, beaten egg, chopped parsley, and optional additions if using. Mix well. Add in flour slowly, stirring to combine. You will have a thick batter. If it seems thin, add a little more flour.
Heat a large skillet over medium heat. Add desired amount of butter and olive oil to cook the batter. Using a spoon, drop batter into 3- or 4-inch circles. Cook until lightly browned, then flip and brown the other side. Transfer to a plate once cooked.
Serve with sour cream, hot sauce, or fresh baby greens. Add salt to taste if needed.