Start by bringing a large pot of water to a boil. Add the udon noodles. Boil for 30 seconds - 1 minute to loosen them. If using dried noodles, cook according to package instructions. Drain, rinse in cold water to remove excess starch, and drain thoroughly again. Set aside.
Place a large Dutch oven, non-stick pot, or large cast iron skillet over medium heat. When the pan is heated, add the butter. Once partially melted, stir in the garlic and dashi granules. Cook for 30 seconds, until the dashi partially dissolves. At this point, the butter should be a light brown color.
Add the drained noodles and toss to coat them in the butter. Cook for 5 minutes over medium heat, until the noodles have dried out and are slightly crisped. Remove and set aside.
Add a tablespoon of oil to the pot, along with the pork shoulder. Brown the pork until crisp on the edges. Add the mushrooms and mirin, and cook until caramelized.
Add the cabbage, carrot, pepper, soy sauce, and water. Stir-fry until the vegetables are wilted, and add the noodles back in, along with the scallions. Stir-fry for another minute. Serve!