Pile the shredded zucchini in a colander and sprinkle with 1 tablespoon of salt. Toss the zucchini well and let stand for 5 minutes. Squeeze out as much liquid as possible and transfer the zucchini to a large bowl. Stir in the eggs, flour, dill, parsley, 1/4 cup of the mint and the feta. Stir in 1/2 teaspoon of pepper and refrigerate the fritter batter for about 10 minutes.
In a food processor, coarsely puree the chopped cucumber. Transfer to a medium bowl. Stir in the yogurt and the remaining 2 tablespoons of mint and season with salt and pepper.
Preheat the oven to 350°. In a medium saucepan, heat 1/2 inch of vegetable oil to 350°. Set a paper towel-covered baking sheet near the stove. Working in batches, drop rounded tablespoons of the fritter batter into the hot oil and fry, turning the fritters a few times, until browned and crisp, about 2 minutes. Using a slotted spoon, transfer the fritters to the prepared baking sheet and repeat with the remaining fritter batter. Discard the paper towels and reheat the fritters in the oven for about 3 minutes. Serve the zucchini fritters hot with the cucumber-yogurt sauce.
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