Mix all slaw ingredients and refrigerate for one hour.
Make 4 equal size patties, season with salt and pepper. Grill patties over high heat, 3-5 minutes per side.
Put 4 piles of pastrami or corned beef in a pan over medium heat. After two minutes, top each pile with a slice of Swiss cheese. Remove when cheese melts.
Pour butter into pan. Toast buns, cut sides down, for two minutes.
Assemble burgers: Place slaw on bottom half of bun. Top with burger, pastrami or corned beef and cheese. Cover with top bun and serve.