For the sauce: Melt the butter in a saucepan, whisk in the flour and cook to golden brown, stirring occasionally. 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. Reheat on low before serving.
Heat half of the oil in a non-stick pan over medium-low heat. Sauté the green pepper and onion until soft. Add in the steak and season with steak seasoning. Cook on low heat for 8 to 10 minutes. Adjust the seasoning with salt to taste.
Slice the buns in half creating a top sheet and a bottom sheet. Don't separate the buns individually.Add the remaining oil as needed to a nonstick pan on medium heat, take the top sheet of the buns and place into the pan, cook until golden brown then remove and set aside. Do the same with the bottoms of the buns.
Place the beef mixture on the buns. Ladle the cheese on top. Portion and serve with pickles.