Preheat to 300°F.
Pat roast dry, season generously with salt and pepper, spread mustard over roast, and rest 15 minutes. Heat oil in a Dutch oven or oven safe pot over medium high heat. Sear roast on all sides 3–4 minutes per side until deeply browned.
Whisk together soy sauce, apple cider vinegar, honey, orange juice, miso paste, chicken broth, pomegranate juice, ginger, garlic, and bouillon paste until smooth.
Pour braising liquid over roast, and top with mushrooms. Liquid should reach about halfway up the meat.
Cover tightly. Bake 3–4 hours until roast is fork tender.
Rest 10 minutes before slicing or shredding. Serve with sauce and mushrooms over rice or mashed potatoes. If you would like the sauce thickened, simmer for 10 minutes before serving.