Roasted Loin of Pork with Mushroom Stuffing and Burgundy Sauce

4 cups beef stock
4 tablespoons olive oil, divided, plus 1/4 cup
1 onion, finely chopped
5 cloves garlic, finely chopped
1 shallot, finely chopped
1 teaspoon grated lime zest
1 pound mixed, fresh mushrooms, finely chopped
1 cup bread crumbs
1/4 cup parsley, chopped
salt and pepper
1 4 pound boneless pork loin
1/2 cup burgundy or other red wine
4 tablespoons butter

In a saucepan, boil stock over medium high heat until reduced by half, to 2 cups. Set aside. Heat 2 tablespoons olive oil in a large skillet over medium high heat. Add onion, garlic, shallot and lime zest. Saute 5 minutes. Add mushrooms and cook until mixture is golden brown, about 10 minutes. Combine in a large bowl with bread crumbs and 1/4 cup olive oil, stirring well. Add parsley, season with salt and pepper and set aside. To prepare pork for stuffing, pat dry. Beginning in the middle of one end, with a thin, very sharp knife, make a lengthwise cut toward center of pork. Repeat from opposite end of pork, to complete a hole running through middle. With the handle of a wooden spoon, or your fingers, open up the cut you have made to about a 2 inch wide opening. Working from both ends of pork, pack stuffing into opening, pushing towards center. Season all sides of the pork with salt and pepper. Heat oven to 375F. Heat 2 tablespoons olive oil in a large skillet over high heat until hot but not smoking. Brown pork on all sides, about 2 minutes. Transfer to a roasting pan, and roast in oven about 1 hour. Remove pork to cutting board and let stand 10 minutes. Meanwhile, on top of stove add burgundy to the roasting pan and deglaze over medium high heat, scraping up any browned bits. Add reduced stock to pan, and simmer, stirring occasionally, 5 minutes. Add butter, 1 tablespoon at a time, to sauce, stirring well. Season with salt and pepper. Slice pork and serve with sauce.