Cook beets in boiling water to cover 30 to 40 minutes or until tender. Drain and peel.
Meanwhile, bring vinegar and next 7 ingredients to a boil in a medium saucepan over medium-high heat. Reduce heat, and simmer 15 minutes.
Slice beets into quarters; pour vinegar mixture over beets. Allow beets to cool to room temperature, cover, and refrigerate several hours or overnight.
Combine yogurt, garlic, and salt; cover and chill until ready to use.
Spread yogurt mixture evenly onto serving platter. Top with beets, parsley, mint, and pomegranate seeds. Drizzle with olive oil.