Trim excess fat from roast and cut into large cubes, about two inches square. Add the meat to a slow cooker or heavy covered, ovenproof pan like a Dutch oven. Pour in water just to cover the top of the meat and sprinkle on ½ envelope McCormick's pot roast seasoning. Cook slowly for several hours until the meat falls apart. Time will vary whether you use the oven or a slow cooker. If cooking in the oven, set the temperature for 300 degrees.
When the meat is cooked and falling apart, use a slotted spoon or spider to remove the meat from the cooking liquid. Discard the liquid. Allow the meat to cool enough to handle, then shred it with your fingers, discarding any fat or gristle.
To a small saucepan add the barbecue sauce, honey, vinegar, and ¼ cup water. Cook over low heat until the sauce is heated through. Set aside.
Butter the hamburger buns and toast under the broiler until barely golden brown. Watch them constantly.
Reheat the sauce in the pan and add the shredded beef. Cook until the beef is just heated through. Spoon the beef onto the bottom half of the bun. If you like, add a little mayonnaise to the top bun before putting it on the sandwich. Shove the sandwiches into little foil pouches if you have them, or just place in a 250 degree oven to keep warm until the fries are ready.
For the French Fries:
Heat cooking oil in a large, heavy pot with straight sides. 2-3 inches of oil is fine. Test the oil by dropping in one piece of raw potato. If it sizzles and floats to the top add the fries in 3 batches. Fry just until the potatoes become limp. Remove partially cooked fries with a spider onto paper towels. Turn off the heat and let the fries cool. Turn the burner on and re-heat the oil. Drop the partially cooked fries into the hot oil and cook until golden brown. Remove from the oil and place on paper towels. Stir the fries around to soak up excess oil and season with coarse salt. Should be served immediately.