The secret to this slowly cooked pot roast is that you add no liquid to the pan. The big sweet onions cook down, and this provides all the juices you need for the beef to simmer. From "The Dinner Doctor" by Anne Byrn.
Place a rack in the center of the oven and preheat the oven to 300 degrees.
Pat the roast dry with paper towels and season it with salt and pepper.
Place the flour in a shallow bowl. Dredge the roast in the flour, then shake off the excess.
Heat the oil in a 5 to 6-quart heavy, covered flameproof casserole or Dutch oven over medium-high heat. Add the roast and brown it on both sides, 3 to 4 minutes per side.
Remove the casserole from the heat, and transfer the roast to a plate.
Place the onion halves, cut-side down, in the bottom of the casserole. Place the roast on top of the onions and cover the casserole.
Bake the beef until it is quite tender and the juices have thickened, 3 to 3 1/2 hours.
One hour before the beef is done, add the carrots and potatoes, if using, to the casserole. Spoon the juices over the vegetables to baste, replace the casserole lid, and return the casserole to the oven.
To serve, carefully remove the roast from the casserole and slice it. Arrange the slices of beef on plates with the carrots, onion, and potatoes, if using, and spoon the pan juices on top.