Season the beef shoulder roast generously with salt and pepper on all sides.
In a large Dutch oven, heat the olive oil over medium-high heat. Once hot, add the beef roast and sear it on all sides until browned, about 4-5 minutes per side. Remove the roast and set aside.
In the same pot, add the chopped onion and garlic. Sauté until the onion is translucent, about 5 minutes.
Pour in the apple cider, scraping up any browned bits from the bottom of the pot.
Add the beef broth, apple cider vinegar, thyme, and bay leaves. Stir to combine.
Return the beef roast to the pot, then add the sliced carrots and diced potatoes around the meat.
Bring the mixture to a simmer, then cover the pot and transfer it to the preheated oven.
Braise in the oven for about 3 hours, or until the beef is tender and easily shredded with a fork.
Remove the pot from the oven, discard the bay leaves, and let the beef rest for 10 minutes before slicing or shredding.
Notes
For added flavor, consider adding a tablespoon of Dijon mustard to the braising liquid.
You can also substitute the beef shoulder with chuck roast for a similar result.
For a thicker sauce, remove the beef once cooked, and simmer the braising liquid on the stovetop until reduced by half before serving.