Preheat the oven to 275 degrees F.
Heat the olive oil in the bottom of a Dutch oven or other large, lidded, ovenproof pot over medium heat. You want enough oil to lightly coat the bottom of the pot.
Mix the ketchup, vinegar, and brown sugar in a small bowl. Set aside.
Sprinkle the beef all over with the salt and pepper, and then place in the heated pot. Brown the beef on all sides, about 2-3 minutes per side. Add the garlic and cook until fragrant but not turning brown, about 30 seconds more.
Add the beef broth, and then pour the ketchup mixture over the browned beef to evenly coat. Lift up the bottom of the roast to let the mixture flow underneath, too.
Bring the liquid to a boil, cover the pot, and then place it in the preheated oven. Bake a 3-pound roast for 3 hours; plan on 4 hours for a 4- to 5-pound roast. The meat should be very tender and fall apart easily.
Serve over mashed potatoes, mashed baked potatoes, or egg noodles, if desired.