Preheat the oven to 325 degrees F.
Season the roasts well on all sides with 2 teaspoons of the salt and the pepper each. Using a paring knife, make 10 small, thin slits total into each of the roasts on all sides, and fill the holes with the garlic cloves. Spread the rosemary amongst the 2 roasts and also stuff into the slits.
Heat a saute-pan over medium-high heat and add two tablespoons of the olive oil. When the oil is hot, working one at a time, sear the roasts until very well browned on all sides, 4 to 6 minutes per side.
Place the roasts in a roasting pan. Add the vegetables, the stock, and cola and tomato paste and blend well. The liquid should come about 1/2 way up the sides of the roast. Cover the pan with foil, place in the oven, and roast until the meat is falling apart-tender, about 3 to 4 hours, adding extra water as necessary to keep the liquid level at about 1/3 up the sides When the meat is fork-tender, remove the roast from the oven and carefully transfer the roast to a serving platter. Cover loosely to keep warm.
Skim off as much of the fat from the surface of the cooking liquid as possible. Reserve 1/4 cup of the fat in a small bowl and add the flour. Stir to make a smooth paste. Slowly whisk this mixture into the hot cooking liquid that remains in the roasting pan and place over high heat on the stovetop. Cook, whisking frequently, until mixture comes to a boil and thickens. Continue to cook for about 5 minutes or until the sauce is thick enough to coat the back of a spoon. Taste and adjust seasoning, if necessary.