Heat 2 tablespoons of the butter in a large skillet over medium-high heat. Add the white, portobello, cremini and oyster mushrooms, season with salt and cook, stirring, until the mushrooms are browned thoroughly, about 5 minutes. Season the mushrooms with the Montreal steak seasoning and Worcestershire sauce. Add the thyme sprigs and cook for 1 minute more. Transfer the mushrooms to a plate and set aside.
Add 2 more tablespoons of butter to the same skillet and throw in the onions and green and red peppers. Reduce the heat to medium low and cook the veggies until dark golden and soft, about 8 minutes.
Preheat the broiler.
Add the black pepper and cayenne to the processed cheese sauce and stir. Microwave according to the package instructions until hot.
To toast the rolls, spread 1 tablespoon of butter on the inside of both the top and bottom of each roll with a butter knife. Place the rolls on a baking sheet butter-side up and broil until golden brown, 3 to 4 minutes.
To build the sandwiches, spread 1 tablespoon of mustard and 1 tablespoon of mayonnaise on the bottom half of each roll. Place a pile of mushrooms onto the bottom of each roll. Top with the peppers and onions and spoon a generous amount of cheese sauce over the veggies. Place the top on the sandwich and serve immediately.