Heat gas grill to med-high heat. (*Oil grates with tongs and wadded papertowel soaked in canola oil if needed to prevent sticking.)Thread mushrooms and onions onto skewers or use a mesh grill basket/pan. Place burgers and skewers onto grill and grill 7-8 minutes. While burgers and veggies are cooking, whisk in bowl the mustard, honey, mayo, vinegar, cayenne and salt & pepper to taste. Stir at least 3 Tablespoons of the sauce into the cabbage mix til well mixed. Set aside. Pour extra sauce into 6 finger bowls. Flip burgers and turn skewers as needed. While second side is cooking (another 5-6 minutes), spread insides of buns with softened butter. When burgers are almost done, place bottoms on grill buttered-side down and toast. Remove veggies and coarse chop. Flip over, top each with a burger, veggies, folded or scrunched bunches of pastrami, and 3 slices of cheese. Place tops onto grill to toast insides. Close lid to melt cheese and warm pastrami. When melted, transfer to a serving platter, pile on coleslaw and top with top buns. Serve with extra sauce for dipping burgers, fries and any extra veggies.