1. Place sun-dried tomatoes and 1 cup water in a microwave-safe bowl; microwave on HIGH 2 minutes. Let stand 3 minutes. Drain. Place sun-dried tomatoes, mayonnaise, 1/4 teaspoon pepper, and 1 garlic clove in a mini food processor; pulse 10 times or until tomatoes are finely chopped. Set aside.
2. Combine remaining 1 garlic clove, 1/4 teaspoon pepper, cheese, salt, and lamb in a large bowl. Divide mixture into 4 portions, shaping into a 1/2-inch-thick patty. Heat a grill pan over medium-high heat. Coat pan with cooking spray. Add patties to pan; cook 4 minutes on each side or until done. Remove from pan; cover and keep warm.
3. Arrange 4 bun halves, cut sides down, in pan over medium-high heat; cook 1 minute or until toasted. Repeat procedure with remaining bun halves. Spread about 1 tablespoon mayonnaise mixture on bottom half of each bun; top each with 1/2 cup arugula, 1 patty, 1 tomato slice, and top half of bun.