Begin by washing the zucchini thoroughly and trimming off the ends. Grate the zucchini using the large holes of a box grater. Place the shredded zucchini into a clean kitchen towel, gather the corners, and squeeze firmly to remove as much moisture as possible.
In a large bowl, combine the drained zucchini with the shredded cheddar and mozzarella cheeses, lightly beaten eggs, flour, garlic powder, smoked paprika, salt, black pepper, and chopped parsley. Mix until everything is well incorporated.
Heat a non-stick skillet over medium heat and lightly grease it. Scoop spoonfuls of the batter into the skillet, flattening them slightly with the back of a spoon. Cook the fritters for about 3-4 minutes on each side or until they are golden brown and cooked through.
Transfer the cooked fritters to a plate lined with paper towels to absorb any excess oil. Serve immediately with the yogurt dip, which is made by mixing the Greek yogurt, lemon juice, honey, and a pinch of salt. Garnish with additional parsley and a lemon wedge for a fresh finish.