Spread one side of each slice of sourdough with butter – these will be the outsides of the sandwiches. Mix the ketchup, mayonnaise and horseradish sauce and spread this over the other sides of the sourdough.
Layer up 2 slices of the bread with the chicken or turkey,followed by the some of the cabbage and, finally, the sliced cheese. Top each sandwich with a remaining sourdough slice(with the butter on the outside) and press down lightly.
Set a frying pan big enough to hold both sandwiches over a medium-high heat. Add the sandwiches, cheese-side down,and fry for 2-3 minutes until deep golden brown, pressing them gently with a spatula from time to time.
Carefully turn the sandwiches and fry on the other side for 1-2 minutes. Remove the sandwiches from the pan, cool for 1 minute, then halve and serve with more cabbage on the side.