BBQ Pulled Mushroom Sliders

Name: BBQ Pulled Mushroom Sliders
Ingredients: 30 ounces king oyster mushrooms, about 9 large mushrooms; 1/3 cup soy sauce; 1/3 cup apple cider vinegar; 1 tablespoon grated garlic, about 3 cloves; 3 teaspoons smoked paprika, divided; 2 tablespoons neutral oil; 1/2 cup BBQ sauce; 1 12-pack Hawaiian rolls; 12 slices of cheese (such as american, provolone, or cheddar); 3 tablespoons unsalted butter; Optional: pickled things for serving, pickles, red onions, pepperoncini, etc. and sesame seeds for topping