Cook's Note: You can substitute 1 1/2 pounds ground beef for the sirloin, brisket and short rib mix.
For the coleslaw: Mix together the vinegar, mayonnaise, mustards, sugar, Worcestershire, salt, garlic, jalapenos, cabbage and onions. Set aside or refrigerate to let the flavors meld, preferably for 1 hour.
For the burgers: Preheat the grill to high heat. Mix together the brisket, short rib and sirloin to combine well and form into 4 equal patties. Sprinkle both sides of the patties with salt. Grill the patties over high heat until medium-rare, 3 to 5 minutes per side.
Divide the pastrami into 4 small piles. Warm the pastrami piles in a saute pan over medium heat. After 2 minutes, top each pile with a slice of Swiss cheese. When the cheese has melted, remove the pastrami from the pan and set aside.
Brush the cut sides of the buns with the butter and toast, cut-side down, in a pan or on the grill.
To serve, place a burger on the bottom bun, top with the pastrami with cheese, a heaping spoonful of the slaw, and finish with the top bun.