In a large bowl, combine the yogurt, 1 tablespoon olive oil, the chili powder, coriander, lemon peel and 1 1/2 teaspoons lemon juice. Season the chicken with salt and pepper, then toss with the yogurt marinade; let stand for 10 minutes.
Preheat the broiler. Position a greased rack on a rimmed baking sheet, then arrange the chicken in a single layer on top; drizzle with 1 tablespoon olive oil. Broil the chicken about 3 inches from the heat for 5 minutes. Turn with tongs, drizzle with another 1 tablespoon olive oil and broil until browned and cooked through, 8 to 10 minutes.
Meanwhile, on another baking sheet, toss the asparagus with 1 tablespoon olive oil, then season with salt and pepper and arrange in a single layer. Broil until just crisptender, about 5 minutes.
Divide the watercress among 4 plates, then top with the asparagus and chicken. Drizzle with the remaining 2 tablespoons olive oil and the remaining lemon juice; season with salt and pepper.