Preheat the oven to 325°F (165°C).
Season the short ribs generously with salt and black pepper. Lightly coat them with flour, shaking off any excess.
Heat a large oven-safe Dutch oven over high heat. Sear the short ribs on both sides until deeply browned. Work in batches if necessary to avoid overcrowding the pot. Transfer the ribs to a plate.
Carefully remove excess grease from the Dutch oven. Add the butter and sliced onions. Cook for about 5 minutes, stirring occasionally, until the onions soften.
Pour in ½ cup of the apple cider. Season the onions with a little salt and pepper and continue cooking for 5–8 minutes, until the cider has evaporated and the onions become lightly golden.
Stir in the fresh thyme.
Return the seared short ribs to the Dutch oven. Pour in the remaining 1½ cups apple cider and the chicken broth.
Add the carrots, smashed garlic, and bay leaves. If using the apple, arrange the quarters around the ribs.
Cover the Dutch oven tightly and transfer it to the oven. Cook for 2½–3 hours, or until the beef is extremely tender and nearly falling from the bone.
Remove the bay leaves. Taste the sauce and adjust the salt and black pepper as needed.
Serve the cider braised short ribs over creamy mashed potatoes. Spoon the caramelized onions and vegetables over the meat, then drizzle generously with the pan sauce.