Remove the chuck roast from the refrigerator 30–45 minutes before cooking. Preheat your oven to 325°F (163°C).
Pat the roast completely dry with paper towels, season all sides generously with salt and pepper, then lightly dust with flour, shaking off any excess.
Heat olive oil in a Dutch oven over medium-high heat until shimmering, then sear the roast 4–5 minutes per side until a deep brown crust forms, searing the edges too. Transfer to a plate and set aside.
Reduce heat to medium, melt butter in the same pot, and add all sliced onions. Cook 15–20 minutes, stirring and scraping up the browned bits, until deep golden brown. Add garlic and cook 1 minute more.
Stir in tomato paste and cook 1 minute, then pour in the apple cider, beef broth, apple cider vinegar, and Dijon mustard, scraping up any remaining browned bits. Tuck in bay leaves, thyme, and rosemary, then bring to a simmer.
Return the seared roast to the pot, nestling it into the onions and liquid (liquid should reach halfway up the sides). Add optional vegetables around the roast, cover, and transfer to the preheated oven for 3 hours.
After 3 hours, check that the internal temperature reads at least 190°F (88°C) and that the meat pulls apart easily with a fork. If not tender, return to the oven and check every 30 minutes.
Transfer the roast to a cutting board, tent with foil, and rest 10–15 minutes. Remove bay leaves and herb sprigs, skim excess fat from the sauce, then slice or shred the meat and serve topped with the onion sauce.