Heat grill to medium. Press pepper into steaks. In a skillet, saute mushrooms in oil and 1 tablespoon of the butter, adding basil or herb of choice. Remove mushrooms and set aside. Melt remaining butter in skillet, then whisk in flour. Whisk in milk over low heat; add cheese. Add mushrooms and keep the sauce warm.
Grill steaks for 3 minutes on each side, or to taste. Serve with mushroom sauce.