in a small bowl, mix the catsup, mustard, cherry pepper, and vinegar and set aside. In a food processor, pulse half of the beef until just coarsely chopped. Transfer to a bowl. Repeat with remaining beef. Toss the beef with 1/2 teaspoons salt and 1/2 teaspoon pepper.
In a large skillet, heat 1 1/2 tablespoons of the oil over medium-high heat until shimmering hot. Add the beef and cook, stirring occasionally, until it loses most of its raw color, about three minutes. Transfer to a plate. Heat the remaining 1 1/2 tablespoons oil in the pan. Add the onion and 1/2 teaspoons salt.
Cook, stirring often, until beginning to soften and Brown, about four minutes. Add the mushrooms and 1/2 teaspoons salt. Cook, stirring often, until they soften and begin to release their juice, about two minutes. Add the catsup mixture and beef and any accumulated juices. Cook, stirring often, until heated through, about two minutes. Stir in the cheese until melted, about one minute longer.
Split the roles almost threw lengthwise and pile on the steak in Aruba. Cut the sandwiches in half and serve. Serves four.