4 boned, skinned chicken breast halves (about 1 1/2 lbs.)
1 1/4 cups plain whole-milk yogurt
1 1/4 teaspoons ground cumin
1 teaspoon fresh lemon juice
About 3/4 tsp. kosher salt
1/2 teaspoon red chile flakes
1/4 teaspoon ground turmeric
About 1 tbsp. vegetable oil
1 English cucumber, cut into 1/4-in. dice
2 tablespoons minced shallot (1 medium)
1/4 cup chopped fresh mint leaves
Freshly ground black pepper
How to Make It
Rinse chicken and pat dry. Trim any fat and remove the tender from each breast (reserve for another use). Working 2 at a time, arrange chicken between layers of plastic wrap. With a meat mallet or rolling pin, pound meat to an even thickness of 1/4 in.
Prepare a grill for direct high heat (about 500°; you can hold your hand 5 in. above cooking grate only 2 to 3 seconds). If using charcoal, spread half-lit coals in firegrate, top with cooking grate to preheat, and let heat build to high.
In a medium bowl, combine yogurt, cumin, lemon juice, 3/4 tsp. salt, the chile flakes, and turmeric. Set aside 1/2 cup yogurt mixture. Add chicken to bowl, flip to coat on both sides, and let sit at room temperature 10 minutes. Transfer chicken to a plate, wiping off excess marinade; rub lightly with oil on both sides.
Using metal tongs, wipe cooking grate with oiled paper towels. Grill chicken, covered, 3 to 4 minutes. Turn over, cover, and cook 2 to 3 minutes more. Transfer to a clean plate and season with salt.
In a serving bowl, combine cucumber, shallot, mint, reserved 1/2 cup yogurt mixture, and salt and pepper to taste. Serve chicken with cucumber salad.