Preheat your oven to 300°F.
In a large Dutch oven, heat the olive oil over medium-high heat. Season the chuck roast with salt and pepper, then sear it in the hot oil until browned on all sides, about 4-5 minutes per side. Remove the roast and set aside.
In the same pot, add the chopped onion and garlic. Sauté for about 3-4 minutes until the onion is translucent.
Add the carrots and celery to the pot, stirring for another 2-3 minutes.
Pour in the apple cider and beef broth, then stir in the tomato paste, thyme, rosemary, and bay leaves. Bring the mixture to a simmer.
Return the seared roast to the pot, ensuring it is submerged in the liquid. Cover the pot with a lid and transfer it to the preheated oven.
Braise the roast for 3 to 4 hours, or until the meat is fork-tender. Check occasionally to ensure there is enough liquid; add more broth if necessary.
Once done, remove the pot from the oven and let the roast rest for about 15 minutes before slicing. Serve with the vegetables and sauce from the pot.