Yes, you can grill avocados!
Cut avocado in half lengthwise and remove pit
Lightly cover in oil and sprinkle with salt and pepper
Over high heat on your grill, lay the flesh side down
Grill for 3 minutes - the point is to get good grill marks on them, and not let them get too soft
Remove from grill and sprinkle grated cheese while still hot so it melts
Get creative - sprinkle bacon, sesame seeds, spicy sauce of choice, or other things