Bring meat to room temperature and pat dry. Cut into 2-inch pieces. Just before cooking, season with Kosher salt and black pepper.
Preheat oven to 325F.
Heat oil, 2 turns of the pan, over medium-high heat in a large Dutch oven. Add the bacon and stir until crisp; remove to a plate. Cook meat in batches, caramelizing on all sides. Remove to a plate and repeat with remaining meat, adding additional oil if necessary.
To meat drippings, add chopped carrot, celery, onion, sliced garlic, marjoram, half the thyme, bay leaves, salt and pepper. Partially cover pot and cook 5-7 minutes, stirring occasionally. Stir in tomato paste, cook for 1 minute, then stir in hard cider or vermouth and a few fat strips of orange rind; deglaze and reduce liquid by half. Add stock then slide meat and bacon back into the pot, bring to bubble, cover and transfer to oven. Roast 2 1/2 hours. Remove the stew and let it stand, covered, while you roast squash.
Raise heat to 425F. Coat squash with oil and toss with remaining thyme, salt, pepper and nutmeg. Roast 30-35 minutes, turning once, until brown at edges.
Once the squash is done, remove bay leaf and orange rind from the stew. Skim fat with a spoon or paper towels.
Place meat in a large shallow bowl or serving dish and stir honey and mustard into sauce. Stir in squash and serve in bowls. Pass crusty bread at table for mopping.