Stir gently to break up the meat pieces in the butter. When the meat has mostly turned from brown to pink, press the Keep Warm button. Add both cans of condensed soup (do not dilute).
Stir gently with a wooden spoon, mixing everything and continuing to break up the meat. Ensure the sealing ring is properly seated around the inside of the lid. Put the lid on and turn it firmly to lock.
Prepare the hoagie rolls by slicing them in half lengthwise if necessary and spreading horseradish sauce on one side and placing a cheese slice on the other side.