Cut off the top 1/2 inch of garlic bulb to expose the ends of the individual cloves. Leaving garlic bulb whole, remove any loose, papery outer layers. Fold a 20x18-inch piece of heavy foil in half crosswise; trim to make a 10-inch square. Place bulb, cut end up, in the center of foil. Sprinkle with basil and rosemary; drizzle with oil. Bring up two opposite edges of foil; seal with a double fold. Fold the remaining ends to completely enclose garlic, leaving space for steam to build.
For a charcoal grill, grill packet on the rack of an uncovered grill directly over medium coals about 30 minutes or until garlic is feels soft when packet is squeezed, turning occasionally during grilling. (For a gas grill, preheat grill. Reduce heat to medium. Place packet on grill rack over heat. Cover and grill as directed.)
Meanwhile, trim fat from steaks. Sprinkle steaks evenly with pepper and salt; rub in with your fingers. While garlic is grilling, add steaks to grill rack. Grill steaks to desired doneness, turning once halfway through grilling. For ribeye steaks, allow 10 to 12 minutes for medium rare (145 degrees F) or 12 to 15 minutes for medium (160 degrees F). For sirloin steak, allow 14 to 18 minutes for medium rare (145 degrees F) or 18 to 22 minutes for medium (160 degrees F).
To serve, cut steaks into six pieces. Remove garlic from foil, reserving basil mixture. Squeeze garlic pulp onto steaks. Mash pulp slightly, spreading it over steaks. Drizzle steaks with the reserved basil mixture.