1. Preheat grill and lightly oil rack. Rinse chicken and pat dry. Whisk together buttermilk, curry, and garlic in a shallow glass dish; season with salt and pepper. Add chicken, turning to coat, and marinate at room temperature, 15 minutes.
2. Meanwhile, soak noodles in boiling water until softened, about 10 minutes. Drain and rinse under cold water; drain well. Toss together noodles, scallions, cucumber, chili sauce, juice, 2 tablespoons mint, and 2 tablespoons nuts; salt and pepper to taste, for noodle salad.
3. Grill chicken over moderate heat, turning once, until cooked through and golden brown, 4 to 5 minutes depending on thickness of cutlets. Transfer to a cutting board and slice. Divide noodle salad among 6 serving bowls. Top with chicken and sprinkle with remaining 2 tablespoons mint and nuts. Serve with lime wedges and garnish with mint sprigs. Makes 6 servings.