1) Salt and drain
Grate the zucchini into a colander set over a bowl. Toss with 1 teaspoon kosher salt and let it sit for 10 minutes.
2) Squeeze hard
Transfer zucchini to a clean towel (or cheesecloth). Twist and squeeze until you get rid of as much liquid as possible. You should be able to wring out several tablespoons. The zucchini should feel fluffy and fairly dry, and clump like damp snow, not drip.
3) Make the batter
In a large bowl, whisk the eggs until smooth. Add squeezed zucchini, Parmesan, scallions, garlic, flour, baking powder, smoked paprika, and black pepper. Mix until you have a thick, scoopable batter. If it looks wet, add 1 to 2 tablespoons more flour.
Salt note: Parmesan brings a lot of salt. Hold off on adding extra to the batter. Taste and adjust at the end if needed.
4) Mix the sauce
In a small bowl, stir together Greek yogurt, lemon juice and zest, olive oil, garlic, and a pinch of salt. Add a splash of water to loosen it to your preferred dip-drizzle situation. Refrigerate until serving.
5) Fry and crisp
Heat a large skillet over medium-high heat. Add enough oil to coat the bottom in a thin layer, about a scant 1/8 inch. When the oil shimmers, scoop 2-tablespoon mounds of batter into the pan and gently flatten into rounds about 2 to 2 1/2 inches wide.
Cook 2 to 3 minutes per side until deep golden and crisp at the edges. Do not overcrowd the pan, work in batches so the oil stays hot. Add a little more oil as needed. Transfer to a wire rack or a paper-towel-lined plate. Taste and season with a pinch of salt if needed.
6) Serve
Serve hot with the lemon yogurt sauce. If you want to get extra, add a squeeze of lemon and a little more Parmesan on top.
