Prep, sweat, and squeeze: Grate zucchini on large holes of a box grater. Toss with 1 tsp salt in a bowl and let sit for 10 minutes.
Transfer grated zucchini to a clean kitchen towel, wrap tightly, and squeeze over the sink to remove as much liquid as possible.
Mix the batter: In a bowl, combine squeezed zucchini, beaten egg, flour, Parmesan, 1 minced garlic clove, and half the dill. Mix until just combined – do not overmix.
Heat the skillet: Place a 10-inch cast iron or heavy skillet over medium-high heat. Add enough oil to cover the bottom by 1/4 inch. When oil shimmers and a pinch of flour sizzles, it’s ready.
Form and fry: Scoop about 2 tablespoons of batter per patty and gently flatten in the pan. Do not crowd – cook 4 patties at a time. Fry 3-4 minutes per side until deep golden brown.
Transfer cooked patties to a paper-towel-lined plate. Sprinkle with flaky salt while hot. Keep warm in a 200°F oven if making a batch.
Make the sauce: Stir together yogurt, remaining minced garlic, lemon juice, and a pinch of salt. Adjust to taste – it should be tangy and bright.
Serve: Arrange patties on a plate, dollop with sauce, and sprinkle with remaining dill. Enjoy immediately.