Preheat the oven to 325°F (163°C).
Pat the 4-pound chuck roast (boneless) dry with paper towels. Season all sides with 1 1/2 teaspoons kosher salt and 1/2 teaspoon ground black pepper.
Place a large pot or Dutch oven over medium-high heat. When hot, add 2 tablespoons canola oil.
Add the roast and brown on all sides, about 4–5 minutes per side, until well browned. Transfer the roast to a plate and set aside.
Reduce the heat to medium. Add 1 yellow onion (diced) to the same pot and cook, stirring, until softened, about 2–3 minutes.
Add 4 cloves garlic (minced), 1 teaspoon fresh thyme (finely chopped), 1 teaspoon fresh rosemary (finely chopped), and 1 teaspoon dried oregano. Stir and cook about 1–2 minutes until fragrant.
Pour in 1/2 cup beef broth and scrape the bottom of the pot with a wooden spoon to deglaze and loosen browned bits.
Add the remaining 1 1/2 cups beef broth, 1 can Dr. Pepper, 2 tablespoons molasses, and 2 tablespoons Worcestershire sauce. Stir to combine.
Return the browned roast to the pot. Add 2 carrots (chopped into 1-inch pieces), 1 lb potatoes (cut into 1-inch-thick pieces), and 1 cup maraschino cherries (whole or halved — pitted). Tuck in 2 bay leaves and place 3 sprigs fresh rosemary on top.
Cover the pot and transfer it to the preheated oven. Cook for 3–4 hours, or until the roast is fork-tender.
When done, remove the pot from the oven. Transfer the roast and vegetables to a serving platter. Remove and discard the 2 bay leaves and the 3 rosemary sprigs.
Strain the cooking liquid into a saucepan or large skillet, discarding solids. Skim and spoon off any fat from the surface of the liquid.
Simmer the strained liquid over medium heat until reduced and slightly thickened to a glaze consistency, about 8–10 minutes, stirring occasionally. (This is your sauce/glaze.)
Slice or shred the roast, serve with the braised vegetables, and spoon the reduced sauce over the meat and vegetables. Garnish with a few of the maraschino cherries from the pot and additional fresh rosemary if desired.