Prepare brine by combining first 5 ingredients in Multipurpose Pot - 8 cup. Bring to a boil, reduce temperature and simmer until sugar dissolves. Set aside.
Cover eggs with water in another Multipurpose Pot - 8 cup. Cover and bring to a boil over medium-high heat. Reduce temperature and simmer gently for 10 minutes.
Drain. Run cold water over eggs until they are cold. Shell eggs and set aside.
Layer peeled eggs with onion rings into a sterilized 2 L glass jar. Slide Bay Leaves down side of jar.
Strain brine and pour over eggs, allowing 1⁄4” headspace. Seal with a sterilized lid.
Store in refrigerator for 1-2 weeks before serving. Serve chilled.