My answer is similar to the others, but just a bit different.
Cut the tenderloin into half inch thick rounds. Season the meat with salt and pepper. Fire up the charcoall grill. While the coals are getting hot, mince thinly slice one sweet onion. Heat a saute pan, or skillet with butter. Place the onion slices on the heated pan and cook for 1 minute over mediu-high heat. Turn and repeat. Remove from the pan. Use one burger-sized portabella mushroom cap for each tenderloin steak (called a tournedo), invert, and drizzle melted butter into the gills. Many people remove the gills. I don't. Season with salt on both sides.
Place the tournedos over the hot coals and cook for two minutes per side. The dripping fat from the bacon will create smoke to flavor the meat. Cooc the mushroom caps, gill side down, over the hot coals at the same time.
Remove the tournedos and mushroom caps. from the grill. Place the cooked onion on top, and then top that with the mushroom cap. If you want, you can drizzle steak sauce on top, but this doesn't really need it.
Option 2:
Same process, except you will cook the food under a broiler.
Seeeeeeya; Cief Longwind of the North