Spray 4- to 5-quart slow cooker with cooking spray. In small bowl, mix salt, pepper, ginger, allspice, cinnamon and garlic. Rub seasoning mixture on beef pieces; set aside. Place onion in cooker; top with beef.
In medium bowl, mix vinegar, tomato paste and brown sugar. Pour mixture over beef. Cover; cook on Low heat setting 9 to 11 hours.
Remove beef from cooker. Transfer sauce to 2-quart saucepan; heat to boiling over medium-high heat, stirring occasionally. Reduce heat; simmer 5 to 8 minutes, stirring occasionally until reduced to about half.
Cut beef against the grain into slices; place on serving platter. Serve with sauce.