4 tablespoons butter, divided
2 tart cooking/baking apples
1 tablespoon brown sugar
1 1/2 tablespoons cider vinegar
1 small to medium rutabaga
Kosher salt and coarsely ground black pepper to taste
Peel onions and cut in half. Slice thinly. Peel and core apples; slice, then julienne into matchsticks about 1/4 inch thick. Toss apples and onions together to combine. Melt 3 tablespoons butter in a large heavy-bottomed skillet over medium-low heat. When butter is melted, add onion-and-apple mixture and allow to cook over medium-low heat, stirring occasionally, for 45 minutes to 1 hour. About 30 minutes into the cooking time, sprinkle 1 tablespoon of brown sugar over the onion mixture and gently stir in.
When onions are deep golden brown and caramelized, add 1 1/2 tablespoons cider vinegar to pan to deglaze it, and stir, scraping up browned bits from bottom of pan. Cook for 1 to 2 minutes longer until vinegar is absorbed, then turn off heat and set aside. While the onion mixture is cooking, wash and peel the rutabaga. Cut into 1/2-inch to 3/4-inch dice. Bring a pot of salted water to a boil and cook diced rutabaga until tender ~ about 20 minutes. Cooking time will vary according to the size of your dice, so test at 5-minutes intervals. The rutabaga is done when it is fork-tender. Drain well.
Remove onion mixture from pan and melt remaining 1 tablespoon butter in the same pan. When melted, add rutabaga cubes. Season with kosher salt and freshly ground black pepper and cook over medium-low heat until heated through, about 10 minutes. Add onion mixture back to pan and gently stir into rutabaga cubes. Let cook for a minute or two to heat through. Serve immediately.