Step 1

Place a rack in middle of oven; preheat to 350°. Cut 1 large red onion into quarters. Thinly slice 1 quarter crosswise and place in a small bowl. Add 3 Tbsp. fresh lemon juice, ¼ tsp. sugar, and a big pinch of kosher salt and stir to combine, breaking up onion. Set aside to pickle.

Step 2

Transfer remaining onion quarters to a food processor and add ½ cup (packed) cilantro leaves, ½ cup (packed) parsley leaves, 2 Tbsp. cornstarch or potato starch, 1½ tsp. Diamond Crystal or 1 tsp. Morton kosher salt, 1 tsp. ground cumin, ½ tsp. baking powder, ½ tsp. ground coriander, ¼ tsp. cayenne, a few grinds of black pepper, and 2 garlic cloves, finely grated. Pulse just until onion is chickpea-size (8–10 pulses). Add 1 large egg, beaten, and two 15.5-oz. cans chickpeas, rinsed, and pulse until chickpeas are coarsely chopped (8–10 pulses).

Step 3

Heat 2 Tbsp. extra-virgin olive oil in a 10" ovenproof skillet, preferably cast iron, over medium-high and swirl to coat bottom and sides. Scrape in falafel mixture and pat into an even layer all the way to the edges of skillet. Cook falafel until starting to turn golden around the edges, about 5 minutes.

Step 4

Transfer skillet to oven and cook until falafel is set on top and browned around the edges, 18–22 minutes.

Step 5

Meanwhile, whisk 1 cup plain whole-milk yogurt, remaining 1 tsp. fresh lemon juice, and a pinch of salt in a medium bowl. If yogurt is thick, thin with water, 1 Tbsp. at a time, to a drizzle-able consistency.

Step 6

Coarsely chop remaining ¼ cup (packed) cilantro leaves and ¼ cup (packed) parsley leaves and place in a medium bowl. Add 3 Persian cucumbers, thinly sliced, 2 radishes, trimmed, thinly sliced, and reserved pickled red onion; season with salt and pepper. Drizzle oil and some of pickling liquid over; toss salad to combine.

Step 7

Run a butter knife around edges of skillet to loosen falafel if needed, then carefully invert onto a plate. Cut into wedges and divide among plates. Serve with salad mounded on top and yogurt drizzled over. Season with more pepper.