In a small bowl, combine oil and garlic. Brush oil mixture onto mushroom slices. For a charcoal grill, grill the mushroom slices on the rack of an uncovered grill directly over medium coals for 8 to 10 minutes or until tender, turning once. (For a gas grill, preheat grill. Reduce heat to medium. Place mushroom slices on grill rack over heat. Cover and grill as above.*)
If you like, spread 4 slices bread or bun bottoms with mayonnaise and top with lettuce and tomato. Add mushroom slices and remaining bread or bun tops. Makes 4 sandwiches.
If grids are wide on you gas grill rack, brush whole mushroom caps with oil mixture and grill whole as above. Slice before serving.