Place the shredded zucchini in a colander over a large bowl or in your sink. Sprinkle 2 tsp salt over the zucchini and toss with your hands. Place a weighted plate on top of the zucchini. Allow to rest for 30 minutes to 1 hour.
Transfer the zucchini to cheesecloth or a kitchen towel. Over the bowl or over your sink, squeeze the zucchini to release any remaining water. Transfer to a medium-sized bowl.
To the zucchini add the flour, Parmesan cheese, garlic, egg, lemon zest, chives, dill, pepper, and ½ tsp of salt. Stir until fully combined.
Heat the oil in a large skillet/saucepan over medium-high heat. Once the oil is shimmering, and working in batches, use an ice cream scoop or large spoon to pull a small mound of the zucchini mixture from the bowl (it should be about the size of a golf ball). Place the mound in the hot oil and use your hand, or a small spatula to gently flatten the fritter to about ¼-inch in thickness. Repeat without over-crowding the skillet.
Cook until the bottoms of the fritters are crispy and golden, about 2 minutes. Use a spatula to carefully flip the fritters and cook for another couple of minutes, or until nicely browned on both sides. Transfer the cooked fritters to a plate lined with paper towels.
Serve with cool sour cream and garnished with extra snipped chives, if desired.