Heat oil and butter in a non-stick pan over medium-low heat. Sauté the green pepper and onion until soft, for approximately 8 to 10 minutes. Add in the very thinly sliced steak and season with steak seasoning. Cook on low heat for 8 to 10 minutes. Adjust the seasoning with salt and pepper to taste.
For the sauce: Melt the butter in a saucepan, whisk in the flour and cook for 1 minute while stirring. Slowly pour in the milk while whisking. Add in the cheese and gently whisk until it is melted, hot, and smooth. Continue to whisk until there are no lumps and sauce has thickened. Season with salt to taste. Cover with a lid and set aside.
Place the beef mixture on the roll. Ladle the cheese on top.