1. Make the kebabs: In a medium skillet, heat oil over medium-high. Add onion and cook until very soft and translucent, about 6 minutes. Add garlic, cumin, and coriander and cook until fragrant, about 2 minutes. Transfer to a large bowl; let cool.

2. In a small bowl, pour milk over bread and let soak 5 minutes. In a large bowl, combine lamb, feta, cilantro, 1 1/2 teaspoons salt, 1 teaspoon pepper, egg, cooked onion mixture, and bread mixture. Use your hands to mix gently until combined (do not overmix). Refrigerate until chilled.

3. Divide meat mixture into 4 equal portions, then form each portion around a 3/4-inch-wide flat metal skewer, leaving about 1 1/2 inches at each end. Transfer kebabs to a baking sheet, cover with plastic wrap, and refrigerate until chilled or up to overnight.

4. Preheat grill for direct-heat cooking (or a grill pan over medium-high). Brush grates with oil. Grill kebabs, turning as needed, until cooked through and charred in spots, and a thermometer inserted into the center reaches 140 degrees (medium-rare), 6 to 8 minutes.

5. Make the sauce: Combine yogurt, cilantro, and lemon zest and juice in a small bowl. Season with salt; drizzle with olive oil. Sprinkle with cayenne before serving.