Pork shoulder, also called Boston butt, is known for its flavor, not tenderness—that is, unless it’s cooked “low and slow.”
In a large Dutch oven on high setting, heat 2 tablespoons olive oil.
Pat pork dry, and season generously with salt and pepper. Sear pork on all sides until well-browned. Remove to a plate.
Reduce heat to medium-high. Add remaining oil. Add vegetables, including garlic. Sauté, stirring occasionally, until golden-brown, about 10 minutes.
Sprinkle flour over mixture and cook, stirring occasionally, 2 minutes.
Add apple cider and stock and bring to a boil. Reduce by one-third, about 20 minutes.
Heat oven to 325º.
Return pork to pot. The liquid should cover one-half to two-thirds of the roast; adjust liquid if necessary. Add rosemary and apples. Cover and place in oven 2-3 hours, or until meat is extremely tender and separates easily with a fork.
Remove pork to a plate and tent with foil.
Skim excess fat from sauce. Add Calvados and raise heat to high; boil 1 minute. Adjust seasoning to taste with salt and pepper.
Carve meat into ½-inch slices and top with sauce. Garnish with parsley. Serve with roasted potatoes or wild-rice pilaf.