To make the cheeseburgers: Prepare grill. Cut six 1/4-inch-thick slices from center of onion and reserve. Divide beef into 6 portions. Form indentation in each portion and spoon rounded teaspoon pesto into each indentation. Form beef portions into six 3/4-inch-thick patties, enclosing pesto completely. Grill patties on an oiled rack set 5 to 6 inches over glowing coals 5 minutes. Turn burgers and grill 3 minutes more. Top burgers with mozzarella and grill 2 minutes more, or until just cooked through. Transfer burgers to a platter and let stand while grilling onion. Brush onion on both sides with oil and grill until softened and browned, about 3 minutes on each side. Spread pesto on both sides of buns and make sandwiches with onion and burgers. To make the pesto: In a food processor blend together all ingredients with salt and pepper to taste until smooth. Pesto keeps, surface covered with plastic wrap, chilled, 1 week. Makes about 1 cup. Serves 6. Gourmet August 1995 Per serving: 4192 Calories (kcal); 317g Total Fat; (68% calories from fat); 179g Protein; 147g Carbohydrate; 772mg Cholesterol; 2068mg Sodium Food Exchanges: 8 1/2 Grain(Starch); 22 1/2 Lean Meat; 2 1/2 Vegetable; 0 Fruit; 51 Fat; 0 Other Carbohydrates Converted by MM_Buster v2.0n.