Step 1Remove giblets and neck from body cavity of turkey. Wash and set aside for gravy. Wash turkey and pat dry with paper towel. Generously season cavity and skin with salt and pepper.
Step 2Stuff neck and body cavity with grapefruits, 2 slices ginger, garlic and rosemary.
Step 3Combine butter, grapefruit zest and remaining slice ginger in small bowl. This will be used for basting, so keep warm.
Step 4Truss turkey, tying wings and legs as close to body as possible with string to keep from burning.
Step 5Arrange mound of charcoal in grill. Light and when covered with gray ash, push half of charcoal to one side of grill and half to other side. Place small roasting pan in center to catch drips. Place turkey on grill over drip pan and cover. Cook until thermometer inserted in thickest part of thigh reaches 165 degrees or until drumstick moves easily when twisted. Begin checking after 1 1/2 hours. Turkey weighing 11 to 12 pounds will take about 2 1/2 hours to cook. Every half hour, add more charcoal to existing piles and baste turkey. If desired, soaked and drained wood chips may be added as well. If turkey browns too quickly, cover affected parts with aluminum foil.
Step 6If using gas grill, leave 1 section of burners unlit. Place small roasting pan in center to catch drips. Heat on high 10 minutes, then reduce heat to medium-low or low. Place turkey on perforated part of broiler pan and place on grill over drip pan and cover. Cook as above, removing broiler pan for last 1/2 hour of cooking.
Step 7Remove turkey from grill, cover loosely with aluminum foil and rest 15 to 20 minutes before carving.