Melt oil and butter in a skillet at medium high heat. Sauté onions until they are golden brown, about 15 minutes, add the mushrooms and saute for about 5 minutes and until all moisture they give off is evaporated; remove from skillet and set aside.

While onions and mushrooms are sautéing, preheat oven to 350 degrees.

Combine the butter, garlic, and paprika. Slice bread lengthwise, spread butter over both sides of the bread. Combine top with bottom and put in oven for 5 minutes; remove from oven and set aside. Turn the broiler on.

Add the beef to the skillet and season it with salt and pepper. Stir the beef just until it is golden brown. Because the meat is sliced thinly this should take no more than 2 minutes. Do not overcook; turn off heat as soon as most of the pink meat has browned.

Slather the horseradish spread on both top and bottom slices of the toasted bread. Pile steak, onions, and mushrooms on bottom slice of bread and top it with cheese slices.

Keep the sandwich open and broil for about 2 minutes or until cheese is bubbly and melted. Watch carefully. Remove the sandwich from the oven, combine the top and bottom pieces together and slice into 4-5 sandwiches. Serve immediately.