Rinse beef shoulder to remove any unwanted residue, pat dry with paper toweling, and place on a utility platter. In a small bowl, make the rub for the beef by combining Smokey Rotisserie Seasoning and Garlic Pepper. Rub the seasonings into all surfaces of the beef, cover with a sheet of plastic wrap and set aside for at least 30 minutes and up to 2 hours at room temperature. (The seasonings will actually begin to "cure" the meat.)
Preheat oven to 425 degrees F.
In an ovenproof skillet heat 1 tablespoon of the oil over high heat, and sear all sides of beef. Cover pan (with lid or foil) and transfer to oven to finish cooking, bringing to an internal temperature of 115 degrees F on an instant-read thermometer, about 30 minutes.
While the beef is in the oven, heat remaining oil over medium-high heat and cook the onions until they are translucent. Add the mushrooms and cook until they soften and begin to give up their juices. Season, to taste, with salt and pepper.
Remove beef from oven and let rest to carryover cook to an internal temperature of 132 degrees F for medium-rare, about 10 to 15 minutes.
Slice beef into steaks, and transfer to serving dish. Top with onion and mushrooms.