Place the grated zucchini in a colander and sprinkle with 1 teaspoon salt. Toss to combine and let it sit for 10 minutes to draw out excess moisture.
After 10 minutes, use a clean kitchen towel or cheesecloth to squeeze out as much liquid as possible from the zucchini. Transfer the drained zucchini to a large mixing bowl.
Add the crumbled feta cheese, eggs, all-purpose flour, chopped dill, chopped parsley, black pepper, and minced garlic to the zucchini. Mix everything thoroughly until 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 and shape it into a small patty. Place the patty in the skillet. Repeat to form more fritters, cooking in batches without overcrowding the pan.
Cook the fritters for 3 to 4 minutes on each side or until golden brown and crispy.
Add more olive oil as needed between batches. Transfer cooked fritters to a plate lined with paper towels to drain excess oil.
Serve the zucchini feta fritters warm, optionally with a dollop of Greek yogurt or a squeeze of lemon.