Preheat oven to 325°. Heat 2 tablespoons olive oil in a large Dutch oven over high heat. Season the pork generously with salt and pepper, then sear it on all sides until thoroughly browned. Remove from pan and set aside.
Reduce flame to a moderately high heat. Add the remaining olive oil, then add mushrooms, shallots, onions, jalapeno pepper, and garlic. Saute, stirring occasionally, until the mixture is golden brown, about 10 minutes. Sprinkle flour over the mixture and cook, stirring occasionally, 2 minutes. Add apple cider and stock or broth, then allow it to boil until reduced by about one-third, about 20 minutes.
Return pork to pan. The liquid should cover one-half to two-thirds of the roast. Adjust the liquid if necessary. Add rosemary and chopped apples, cover pan, and bake in oven 2 to 3 hours, or until the meat is extremely tender and separates easily with a fork.
Remove pork from pan; keep warm. Skim excess fat from the sauce. Add Calvados or applejack to sauce, then bring to a boil 1 minute. Adjust seasoning with salt and pepper.
To serve, carve meat into ½-inch slices and top with sauce. Garnish with parsley and serve with roasted potatoes or wild rice pilaf.