Place oil in a large dutch oven and heat over medium-high. Add salt pork, onion, carrot, shallot and garlic and cook until lightly browned.
Remove the vegetables and set aside.
Brown the chicken, a few pieces at a time. Place browned pieces on a platter as you work. Once all the chicken is browned, add the chicken and vegetables back in the pan including any accumulated juices. Pour the brandy over the mixture (if using). Sprinkle the flour over the chicken and stir to combine. Add all the rest of the ingredients except the mushrooms and bring the mixture to a simmer. Cover the pot and simmer on low for about 1 hour until the chicken is cooked through.
Add the mushrooms during the last 5 minutes of cooking.
To serve, place the chicken on a warmed platter and top with the vegetables and sauce.