1. Wash plums. Cut plums in quarters, and remove pits. Place plums in an 8-qt. stainless steel or enameled Dutch oven; crush plums with a potato masher. Add 2 cups water, star anise, and cinnamon sticks. Bring to a boil; cover, reduce heat, and simmer 20 minutes or until fruit is soft.
2. Line a wire-mesh strainer with 2 layers of damp cheesecloth or a jelly bag. Place over a bowl. Pour plum mixture into srainer, and let drain 30 minutes or as needed to extract 3 cups juice. (Do not press or squeeze mixture.) Discard solids.
3. Sterilize jars, and prepare lids.
4. While jars are boiling, cut vanilla beans in half lengthwise. Scrape out and reserve seeds. Set aside vanilla bean pods for another use (such as Bottomless Vanilla Extract). Stir together 3 cups juice, vanilla bean seeds, and pectin in clean 8-qt. Dutch oven. Cook over high heat, stirring constantly, until mixture comes to a rolling boil. Stir in sugar; return to a rolling boil. Boil hard exactly 1 minute, stirring constantly. Remove from heat, and let foam settle (about 1 minute). Skim off and discard any foam.
5. Fill, seal, and process jars, leaving 1/4-inch headspace and processing 10 minutes.
6. Remove jars from water, and let stand, undisturbed, at room temperature 24 hours. To check seals, remove the bands, and press down on the center of each lid. If the lid doesn't move, the jar is sealed. If the lid depresses and pops up again, the jar is not sealed. Store properly sealed jars in a cool, dark place up to 1 year. Refrigerate after opening.