Prepare a medium-hot fire in a charcoal grill with a cover, or preheat a gas grill to medium-high
Mushrooms:
Place butter into a skillet over medium-high heat, add the mushrooms and saute till mushrooms start to caramelize (about 5 minutes). Sprinkle with salt and black pepper. Remove from heat cover and reserve
In a medium size, bowl combine the apple, brown sugar, chili powder, and garlic powder and set aside.
To make Fondue Cheese Sauce
Place the shredded cheese and cornstarch in a plastic zip top bag. Seal and shake until the cheese is well coated with cornstarch. Reserve until needed.
Place garlic and wine into a 3-quart pot. Cook over medium heat until it reduces down to one Cup. (remove garlic)
Add lemon juice, nutmeg, and white pepper.
Slowly stir the cheese into the wine(adding cheese a handful at a time). Stir in a figure eight pattern to prevent the cheese from seizing and balling up. Once the cheese is melted and creamy it is ready to serve and should be kept over very low heat and stirred regularly until ready to put on burgers.
To make the patties:
Combine salt and pepper with the ground chuck. Divide the meat into 6 equal portions and form them into patties.
Place patties on the grill. Cook for 4 to 5 minutes per side for medium. Remove from heat and let rest 3 to 5 minutes before serving. Place the rolls, cut side down, on the outer edges of the grill rack to toast lightly during the last
minute of grilling
To assemble, spread cut side of bottom half of roll with cheese sauce, add burgers, then a generous portion of mushrooms, top with more cheese and then a handful of apple slaw. Top with top half of roll.