Preheat the oven to 350°F.
Heat the olive oil in a large skillet over medium-high heat.
Season the beef roast evenly on all sides with the salt and ground black pepper.
Place the seasoned roast in the heated skillet.
Sear the roast on all sides until evenly browned.
Transfer the seared roast to the center of a large baking dish or roasting dish.
Arrange the baby carrots, red potato pieces, and onion wedges around the roast.
In the same skillet, reduce the heat to medium.
Add the minced garlic to the remaining oil and browned bits in the skillet.
Sauté the garlic for approximately 30 seconds, stirring constantly to prevent burning.
Whisk in the red cooking wine, beef broth, and Worcestershire sauce.
Stir well to combine, scraping the bottom of the skillet to incorporate any browned bits.
Bring the sauce mixture to a light boil.
Carefully pour the sauce mixture over the roast and vegetables in the baking or roasting dish.
If using a roasting dish, cover it with the lid.
If using a baking dish, cover it tightly with aluminum foil.
Bake for approximately 3 hours, or until the beef is tender and the vegetables are fully cooked.
Remove the dish from the oven.
Allow the roast to rest for several minutes before slicing or shredding.
Serve the beef roast warm with the carrots, potatoes, onions, and sauce.