Bring meat to room temperature and pat dry. Cut into 2-inch pieces. Just before cooking, season with Kosher salt and black pepper.
Pre-heat oven to 325°F.
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 1 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 425°F. 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.