Sprinkle chicken with 1/8 teaspoon salt and 1/8 teaspoon black pepper. Place chicken in a large resealable plastic bag set in a shallow dish. In a small bowl, combine 1/4 cup of Nectar, 2 Tablespoons of preserves, 2 Tablespoons mint, 1 Tablespoon of oil, vinegar, curry powder and garlic. Pour over chicken; seal bag. Refrigerate for 2 to 4 hours.
Using a gas grill, preheat grill, reduce heat to minimum, place chicken on grill. Grill, covered, 12 to 15 minutes or until chicken is no longer pink (180 degrees F), turning once halfway through grilling. Add apricots to grill, cut side down, during last 5 minutes of grilling or until lightly browned.
For sauce: In a small bowl, combine remaining 1/4 cup apricot nectar, 4 Tablespoons preserves, 2 Tablespoons mint, 1 teaspoon olive oil, the green onions, 3 Tablespoons pistachios, the mustard, mustard seeds and 1/4 teaspoon salt.
Drizzle sauce over chicken and apricots. Sprinkle with remaining nuts.