In a large, shallow saucepan, combine the tomato paste, brown sugar, molasses, garlic powder, onion powder, mustard powder, cinnamon, allspice, Worcestershire sauce, vinegar, salt, and water. Bring to a low boil over medium heat, stirring occasionally to prevent burning. Cook for 25-30 minutes, until reduced by about a quarter. The ketchup should be thick and spreadable. Let cool completely.
Transfer to a clean, airtight container and store in the refrigerator. The ketchup should keep for up to 3 weeks.