Place the grated zucchinis in a colander, sprinkle with salt, and let them sit for about 15 minutes to draw out excess moisture. After 15 minutes, squeeze the zucchinis to remove as much liquid as possible.
In a medium saucepan, bring 2 cups of water to a boil. Slowly whisk in the cornmeal, stirring constantly to prevent lumps. Reduce heat to low and cook for about 5 minutes, stirring frequently until thickened. Remove from heat and let cool slightly.
In a large mixing bowl, combine the cooked polenta, squeezed zucchini, Parmesan cheese, flour, eggs, black pepper, garlic powder, onion powder, and parsley (if using). Mix until well combined.
Heat about 1/4 inch of vegetable oil in a large skillet over medium heat. Once the oil is hot, drop spoonfuls of the zucchini mixture into the skillet, flattening them slightly with the back of the spoon.
Fry the fritters for about 3-4 minutes on each side or until golden brown and crispy. Remove from the skillet and place on paper towels to drain excess oil.
Serve warm with your favorite dipping sauce or yogurt.