Rinse and drain mushrooms, then rub lightly with oil.
Lay the mushroom caps, cup (gill) sides down, on a barbecue grill over a solid bed of hot coals or high heat on a gas grill (you can hold your hand at grill level only 2 to 3 seconds); close lid on gas grill.
Cook until juices start to drip from the mushroom caps, about 5 minutes. Turn caps over and continue to cook until mushrooms are flexible and no longer firm when pressed, 5 to 7 minutes longer.
Lay an equal portion of the red peppers in each cap and cover with cheese. Continue cooking until cheese melts, about 3 minutes.
As cheese melts, split buns, butter if desired, and lay cut sides down on grill until lightly toasted.
Set a mushroom cap on each bun base, season with salt and pepper to taste, add a mound of watercress, and cover with the bun top.