Place all ingredients for the pesto sauce into blender and blend until smooth. Taste, add salt, pepper and lemon juice as needed.
Mix beef with garlic, salt and pepper. Divide beef into 4 even-sized balls and shape each ball into a 1/2 inch thick rectangle. Grill burgers to desired doneness, then add fresh mozzarella slice on top of burger and melt slightly. Remove and cover with foil to keep warm. Toast bread slices on grill.
To assemble the burgers, spread pesto on baguette, top with burger, place a basil leaf or two on mozzarella, then tomato. Serve immediately. Serves 4.