Combine ground beef and pesto in medium bowl; mix lightly, but thoroughly. Lightly shape into twelve 1/2-inch thick patties.
Heat large nonstick skillet over medium heat until hot. Place 6 patties in skillet. Cook 8 to 10 minutes to medium doneness (160°F), turning occasionally. During last 2 minutes of cooking, spoon 1 heaping tablespoon diced tomato mixture on each patty; top with one quartered cheese slice and cover. Repeat with remaining patties. Place burgers on bottoms of rolls; close sandwiches.
Nutrition information per serving: 686 Calories; 261 kcal Calories from fat; 29 g Total Fat; 10 g Saturated Fat; 4 g Monounsaturated Fat; 106 mg Cholesterol; 968 mg Sodium; 58 g Total Carbohydrate; 3.4 g Dietary Fiber; 44 g Protein; 6.8 mg Iron; 11.5 mg Niacin; 0.5 mg Vitamin B6; 2.4 mcg Vitamin B12; 7 mg Zinc; 44.5 mcg Selenium; 93.6 mg Choline;