Trim green tops from beets, leaving 1 inch of stems attached (do not trim root end). Place beets in a large pot. Add water to cover by 2 inches. Boil until beets are tender, about 1 hour. Drain and rinse under cold water to cool. Peel and trim beets. Cut into quarters. Pack into a clean, hot 1-quart jar.
Meanwhile, bring vinegar and remaining ingredients to a boil in a small saucepan over high heat, stirring until sugar is dissolved. Remove from heat, cover, and let syrup steep for 1 hour.
Remove star anise from syrup and return to a boil over high heat. Pour syrup over beets, leaving 1/2 inch space on top. Shake to dislodge any air pockets. Wipe rim, seal, and process jar in a boiling water bath for 30 minutes. Allow at least a week to pickle before eating.
