Trim fat from roast. Coat a Dutch oven with cooking spray; place over medium heat until hot. Add roast; cook until browned on all sides, turning frequently. Remove roast from pan; wipe drippings from pan with a paper towel.
Combine catsup and next 7 ingredients, stirring well. Return roast to pan, and pour catsup mixture over roast. Bring to a boil. Cover, reduce heat, and simmer 4 hours or until meat is tender. Remove roast from pan, reserving sauce in pan. Let roast cool slightly. Shred meat with 2 forks, and return to pan. Cover and cook over medium heat until thoroughly heated, stirring occasionally.
Combine cabbage and carrot. Combine vinegar and next 4 ingredients in a saucepan; bring to a boil, stirring occasionally. Boil 1 minute. Pour over cabbage mixture, and toss gently. Spoon about 1/2 cup meat mixture on bottom half of each bun; top each with 1/4 cup cabbage mixture and a remaining bun half.