For marinade, combine wine, garlic, herb, Worcestershire sauce, and oil. Place veal chops in a large plastic bag set in a shallow dish. Pour over chops; close bag. Marinate at room temperature for 15 minutes. (Or, marinate in refrigerator for up to 24 hours, turning bag occasionally.)
Drain veal chops, reserving marinade. Sprinkle chops with freshly ground black pepper. Grill chops on the rack of an uncovered grill directly over medium heat to desired doneness, turning and brushing with marinade halfway through cooking. (Allow 12 to 14 minutes for medium-rare and 15 to 17 minutes for medium doneness.)
Meanwhile, carefully remove stems from mushrooms; chop stems for another use or discard. Brush mushroom caps with reserved marinade; place mushrooms, stem sides down, on grill rack. Grill for 4 minutes. Turn stem sides up; spoon some pesto into each. Grill about 4 minutes more or until heated through. Serve mushrooms with veal chops. Makes 4 servings.