Place the grated zucchini in a large bowl and sprinkle with salt. Toss to combine and let sit for 10 minutes to draw out excess moisture.
After 10 minutes, place the zucchini in a clean kitchen towel or cheesecloth and squeeze firmly to remove as much liquid as possible.
Transfer the drained zucchini back to the bowl. Add the crumbled feta cheese, eggs, flour, chopped dill, chopped parsley, black pepper, and minced garlic. Mix until all ingredients are well combined.
Heat 1 tablespoon of olive oil in a large non-stick skillet over medium heat.
Scoop about 2 tablespoons of the zucchini mixture for each fritter and gently flatten it into a patty shape.
Place the fritters in the skillet, cooking in batches without overcrowding. Fry for 3-4 minutes on each side or until golden brown and cooked through.
Add more olive oil to the skillet as needed between batches.
Transfer cooked fritters to a plate lined with paper towels to drain excess oil.
Serve warm with a side of yogurt or tzatziki sauce if desired.