Toast the rye until crisp, then cool it completely on a wire rack.
Stir the mayonnaise, horseradish and black pepper together and spread it over one side of each toast slice.
Layer 4 toast slices with half the roast beef, 4 cheddar slices and half the arugula.
Add the middle toast slices spread-side up, then layer on the remaining beef, cheddar, arugula and tomato.
Close with the final toast slices, secure each club with 4 picks and press only hard enough to steady it.
Cut each sandwich into 4 triangles with a serrated knife.
