Pre-heat oil in a large skillet over medium high heat until shimmering. Add ground beef and brown 5 minutes, breaking into chunks. Toss in the onions and pepper and saute for 3 to 4 minutes. Slowly add the steak sauce and beef stock. Simmer until sauce reduces by half, about 5-10 minutes. Reduce heat to low.
In another medium skillet, or on a flat griddle, melt 1 tbs butter over medium heat. Toast rolls.
Serve mixture over rolls with a slice of cheese melting on top.