Add water, cubed beetroot, granulated sugar, cloves, green cardamoms, cinnamon stick, and black cardamom to a saucepan.
Bring the mixture to boil over high heat. Reduce the heat to low and simmer the mixture for 2-3 minutes. Remove the pan from the heat and cool the mixture.
Add peeled and washed pearl onions to a non-reactive jar (a glass jar is preferable).
Pour white vinegar, salt, and the water mixture that we made earlier over the onions and stir gently. Cover the jar with a lid and refrigerate it. Use the onions after 24 hours for up to 10 days.