Remove the pork shoulder from refrigeration 45-60 minutes before cooking to bring it to room temperature. Pat completely dry with paper towels.
In a small bowl, combine salt, pepper, rosemary, thyme, cinnamon, and nutmeg. Rub this mixture generously over all surfaces of the meat, pressing it in to adhere.
Heat olive oil in a large Dutch oven over medium-high heat until shimmering. Place the seasoned pork shoulder fat-side down and sear until deeply golden brown, about 4-5 minutes. Rotate and continue browning on all sides, about 12-15 minutes total.
Remove the browned pork from the pot and reduce heat to medium. Add sliced onions to the rendered fat and sauté until translucent, about 3-4 minutes. Add garlic and cook for 30 seconds until fragrant.
Pour in apple cider, scraping up all the browned bits from the bottom of the pot. Add apple cider vinegar, maple syrup, and bay leaves, then bring the mixture to a simmer.
Return the seared pork to the pot, fat-side up. The liquid should come about halfway up the sides of the meat. Cover with a tight-fitting lid and simmer gently for 3 hours on low heat. Alternatively, transfer to a 325°F oven.
After 3 hours, add the apple wedges around the pork. Cover and continue cooking for an additional 30-60 minutes, until the meat is fork-tender and registers 195°F internally.
Remove the pork from the braising liquid and tent loosely with foil. Allow it to rest for 15-20 minutes.
Meanwhile, skim excess fat from the surface of the braising liquid and simmer uncovered for 10-15 minutes to reduce into a more concentrated sauce. Remove bay leaves before serving.
Serve the tender pork with the reduced sauce, apples, and onions.