In a medium bowl, stir together the garlic, gochujang, mirin, soy sauce, ginger and sesame oil. Add the pork and let marinate at room temperature for about 30 minutes or cover and refrigerate up to overnight.
Preheat the oven to 200 degrees F.
Heat a large skillet over medium-high heat. Spread the cut sides of the rolls with the butter. Toast the rolls cut-side down, gently pressing on them so the centers toast as well, until lightly golden, about 1 minute. Transfer the rolls to the oven to keep warm.
Wipe out the skillet and return it to the stove. Add the vegetable oil and heat over medium-high heat. Add the pork and cook, stirring occasionally, until the meat is cooked through and golden and lightly charred in spots, about 5 minutes. Add the onion, mushrooms and chiles and cook, stirring occasionally, until the onions and mushrooms have softened slightly, about 2 minutes. Divide the mixture into 2 mounds in the skillet and top each mound with half the cheese. Cover the skillet and cook just until the cheese melts, about 1 minute.
Scoop each mound onto a roll, sprinkle with some scallions, sesame seeds, gochugaru and pickled jalapenos.