For this burger recipe, buy mushrooms with stems trimmed, or trim the stems and save for other uses.
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.
* Percent Daily Values are based on a 2,000 calorie diet. Your daily value may be higher or lower depending on your calorie needs.