Heat oil in a large Dutch oven over medium-high heat. Add half of the pork; sauté 5 minutes or until browned. Remove from pan. Add remaining pork; sauté 5 minutes or until browned. Remove from pan. Add onion and mushrooms to pan; sauté 4 minutes. Return pork to pan; add carrot and next 7 ingredients (carrot though beer). Bring to a boil; reduce heat, and simmer 1 hour or until pork is tender.
Combine cornstarch, vinegar, and mustard in a small bowl, and stir with a whisk. Add to pork mixture, and bring to a boil. Cook 3 minutes, stirring frequently. Serve with rice. Garnish with sage sprigs, if desired.