Heat oven to 375°F. Bake biscuits as directed on bag; place on cooling rack. Brush biscuits with 1 teaspoon dressing; cool completely. Set aside.
Heat gas or charcoal grill. Carefully brush oil on grill rack. Mix turkey, 3 tablespoons dressing and the onion. Shape mixture into 2 patties. Place on grill over medium heat.
Cover grill; cook 12 to 15 minutes, carefully turning once, until thermometer inserted in center of patty reads 165°F. Top patties with cheese. Cover and grill about 1 minute longer or until cheese is melted.
On 2 serving plates, split biscuits. Place lettuce leaves on bottom halves; top with burgers and bell pepper strips. Drizzle with additional dressing. Top with remaining biscuit halves.