Prepare the slaw: In a medium bowl, mix together the cabbage, garlic, onion, jalapeno, vinegar, mustard, mayonnaise, sugar, salt, Worcestershire sauce and ShaSha Sauce. Cover and refrigerate 1 hour.
Make the burgers: Build a charcoal fire or heat a gas grill. On a work surface, combine the meats and form the burgers into 4 equal-size patties. Season liberally with salt and pepper.
Grill the burgers over high heat until medium rare, 3 to 5 minutes per side.
Meanwhile, heat a large saute pan over medium heat. Place 4 heaping piles of pastrami in the pan. After 2 minutes, top each pile with a slice of Swiss cheese. Remove them when the cheese is melted; set aside.
Pour the butter into the pan. Place the buns in the pan, cut-side down, and toast, about 2 minutes.
Place a heaping tablespoonful of the slaw on the bottom half of each bun. Top with a burger and a mound of pastrami and cheese. Cover each with the top half of the bun and serve immediately.
In a food processor, puree the peppers, garlic, mustard and vinegar.
Pour the puree into a nonreactive saucepan, then add the sugar and bring it to a boil over high heat. Lower the heat and simmer the mixture for 30 minutes.
In a small bowl or juice glass, mix the flour and 1/2 cup water to make a smooth paste. Whisk it into the pepper mixture and continue to simmer for 20 minutes, stirring regularly, until it becomes very thick. Let the sauce cool, then pour it into a covered nonreactive container (such as a glass jar). The sauce can be refrigerated for up to 1 month.
Photograph by Andrew Mccaul
Recipe courtesy Michael Symon for Food Network Magazine