Mix shrimp and peppers with 3 tablespoons of the Balsamic Vinaigrette in a medium-size bowl. Refrigerate mixture, covered, for 1 hour.
Place large cast-iron or stove-top grill over medium heat. Coat grilling surface with nonstick vegetable-oil cooking spray. Add shrimp and peppers in a single layer. Cook, tossing or turning occasionally, 6 minutes or until shrimp are pink, curled and firm-tender and peppers are firm-tender. Remove to clean bowl; keep warm. If grill is too small to fit all of the shrimp and peppers in one layer, grill mixture in two batches.
Meanwhile, place 4 tablespoons of Balsamic Vinaigrette in a small saucepan. Heat to boiling over low heat. Pour over shrimp-and-pepper mixture in bowl, tossing until well coated.
Serve over hot rice, cooked following package directions.
Stir together oil, balsamic vinegar, red wine vinegar, brown sugar, oregano, rosemary, salt, crumbled thyme and ground black pepper in small bowl.