4 12-to 14-ounce boneless Muscovy duck breast halves trimmed of excess fat
4 teaspoons chopped fresh thyme, divided
2 teaspoons freshly ground black pepper, divided
1 1/2 teaspoons salt, divided
6 firm but ripe Santa Rosa plums or other purple plums, halved, pitted
1 tablespoon extra-virgin olive oil
1/2 teaspoon sugar
Using sharp knife, score skin of duck breasts in crisscross pattern (cut skin only; do not cut through meat), spacing cuts 1 inch apart. Sprinkle duck breasts on both sides with 1 teaspoon thyme, 1 teaspoon pepper, and 1 teaspoon salt. Cover and chill.
Prepare barbecue (medium-high heat). Toss plum halves, olive oil, sugar, 1 teaspoon thyme, remaining 1 teaspoon pepper, and 1/2 teaspoon salt in medium bowl. Grill plum halves, cut side down, until grill marks appear and plums begin to soften, about 4 minutes. Turn plums over and grill, skin side down, until skin begins to soften but plums still retain their shape, about 4 minutes. Transfer plums to bowl. Cover with foil and let stand while cooking duck.
Heat 2 large skillets over medium-high heat. Add 2 duck breasts, skin side down, to each skillet. Cook until skin is crisp and golden, about 7 minutes. Turn duck breasts over and cook to desired doneness, about 8 minutes longer for medium-rare. Remove from heat and let duck rest 5 minutes.
Thinly slice duck crosswise. Divide among plates. Place 2 plum halves alongside each serving. Drizzle any plum juices from bowl over. Sprinkle with 2 teaspoons thyme and serve.
Ingredient tip: We use Muscovy duck breasts in this recipe because they are tender and full-flavored. Look for them fresh or frozen at some supermarkets or order them at dartagnan.com.