Grate the zucchini using the large holes of a box grater into a large bowl. Sprinkle with kosher salt, mix well, and let sit for 10 minutes to draw out moisture.
Transfer the zucchini to a clean kitchen towel and wring it tightly over the sink to squeeze out as much liquid as possible. The zucchini should feel dry and clump together.
Return the dried zucchini to the bowl and add the beaten egg, all-purpose flour, minced garlic, chopped dill, Parmesan cheese, and black pepper. Stir until just combined into a thick, cohesive batter.
Heat 2 tablespoons of olive oil in a large non-stick skillet over medium heat until it shimmers.
Drop heaping tablespoons of the batter into the hot skillet, flattening each gently with the back of the spoon to form 3-inch wide patties.
Cook for 3-4 minutes per side, or until each fritter is deeply golden brown and crisp on the edges. Work in batches to avoid overcrowding the pan.
Transfer the cooked fritters to a plate lined with paper towels to absorb any excess oil.
Serve immediately with a dollop of sour cream on top.