Pat the beef chuck roast dry with paper towels and season generously with salt and black pepper.
In a large bowl, combine beef broth, cranberry juice, balsamic vinegar, brown sugar, and Dijon mustard. Stir well to mix.
Heat olive oil in a large Dutch oven over medium-high heat. Sear the roast on all sides until browned, about 4-5 minutes per side. Remove from pot and set aside.
In the same pot, add chopped onion and minced garlic. Sauté until the onion is translucent, about 3-4 minutes. Pour in the cranberry balsamic mixture and stir.
Return the beef roast to the pot, ensuring it is submerged in the liquid. Cover and transfer to the preheated oven.
Braise the roast for 180 to 240 minutes until tender. Let it rest for 10-15 minutes before slicing.