Set a cast-iron griddle or 12-inch cast iron skillet over medium heat.
Add the rolls, in batches if necessary, and toast lightly on both sides so they’re just crisp on the outsides. Set aside.
Pour the oil into the skillet.
Add onion and pepper and cook, stirring frequently with a spatula, until onions are browned and becoming translucent, 3 to 4 minutes.
Add mushrooms, oregano, paprika, garlic powder, onion powder, and salt. Stir to combine well.
Cook, stirring every few minutes, until well-browned and cooked through, about 10 minutes. Mushrooms will give off some liquid at first, and then the liquid will cook away. After that, they’ll begin to brown. Keep going until they’re as dark and tender as you like.
Off the heat, spoon in about ⅓ cup of the vegan cheese sauce and stir to combine.
Open each roll partway, leaving a hinge of about ¼ inch on one side. Place some of the mushroom mixture into each roll and top with additional cheese sauce.
If you like, serve with yellow mustard, ketchup, and any additional toppings (pickle slices, hot peppers, or hot sauce, for instance.)