Heat a large stockpot or Dutch oven over medium-high heat. Add 2 tablespoons oil. Add the carrots and onions and saute until they begin to caramelize. Next, add the ginger, garlic and habanero. Saute until the vegetables become aromatic, about 1 minute. Add the remaining 2 tablespoons oil and the mushrooms and cabbage. Stir in the tamari sauce, chicken stock and pork. Reduce the heat to low, cover and let simmer about 20 minutes.
To serve, divide the prepared noodles between 4 entree-size bowls. Ladle the soup into the bowls and garnish each with cilantro leaves, bean sprouts and lime wedges. Drizzle with additional tamari sauce, if desired.
Preheat the oven to 425 degrees F.
In a small bowl, mix the olive oil, garlic, salt, and pepper. Using a pastry brush, spread the mixture all over the pork shoulder.
Set the meat on a rack set into a roasting pan. Roast for 20 minutes, and then reduce the heat to 325 degrees F. Continue to cook until an instant-read thermometer inserted into the shoulder reads 185 degrees F, about 4 hours. Remove the pork from the oven and let stand until cool enough to handle, about 30 minutes.