In a small bowl or blender, combine the mayo, ketchup, mustard, a few drops of Worcestershire, and a pinch of salt.
Spread about half of the Russian dressing on the inside of each slice of rye bread. Layer 3/4 of the cheese on the bottom, then the turkey. Spread the sauerkraut over it all, then top with the remaining 1/4 of the cheese. Place the second piece of bread, dressing side down, on top of the sandwich.
In a small nonstick or castiron pan, melt 2 teaspoons of the butter oven medium-low heat. Carefully transfer the sandwich to the pan and cook slowly. The cheese should melt within about 10 minutes and bottom side should become golden brown. Add remaining 2 teaspoons of butter to the pan and flip your sandwich, cook for an additional 5 - 10 minutes.