With food processor or blender running, add garlic through feed tube or lid. Process or blend until garlic is finely chopped. Add basil, thyme, rosemary, and mint. Cover and process or blend until herbs are chopped. With food processor or blender running, add oil in a thin, steady stream. (When necessary, stop food processor or blender and use a rubber scraper to scrape the sides of bowl or container.) Stir in salt and pepper.
Spread some of the herb mixture evenly over both sides of the steaks and over cut sides of tomatoes; set aside. Fold an 18x12-inch piece of heavy foil in half to make a double thickness of foil that measures 9x12-inches. Place asparagus in the center of the foil. Add remaining herb mixture, turning asparagus to coat evenly.
Grill steaks and asparagus (on foil) on the rack of an uncovered grill directly over medium heat for 5 minutes. Turn steaks and asparagus spears; add tomatoes to grill. Grill until steaks are desired doneness. (Allow 3 to 7 minutes more for medium-rare and 7 to 10 minutes for medium doneness.) Grill vegetables until asparagus is crisp-tender and tomatoes are hot (do not turn). Makes 4 servings.