In a small bowl, mix together the prepared horseradish, mayonnaise, and Worcestershire sauce. Season with salt and pepper; set aside.
Top each slice of bread (lightly toasted) with a bit of horseradish mayo. To four of the bread slices, add one slice of cheese, followed by the sliced roast beef, pickles, roasted red peppers, a sprinkle of oregano, salt, and freshly ground black pepper, and one more slice of cheese. Complete the sandwiches with the four remaining slices of bread, horseradish mayo-side down.
Butter both sides of the completed sandwiches.
Set air fryer to 375 degrees F and cook sandwiches, one at a time, for 3 mins per side, or until cheese is melty and bread is toasted. Let sandwiches cool for 1-2 minutes before serving.