1. Drain liquid from beets into a small saucepan, reserving the beets for another use (for instance, use them for Grilled Buffalo Steak with Radicchio-Beet Skewers). Add vinegar, sugar, salt, bay leaves and cloves to the pan. Bring to a boil over medium-high heat, stirring occasionally, until the sugar dissolves. Pour the pickling liquid into a large deep bowl and stir in onions; set aside to cool for 1 hour.
2. Meanwhile, place eggs in a single layer in a saucepan; cover with water. Bring to a simmer over medium-high heat. Reduce heat to low, cover and cook at the lowest simmer for 10 minutes. Pour off the hot water and run cold water over the eggs until they are completely cooled. Peel the eggs.
3. When the pickling liquid is cool, place the peeled eggs in a 4-cup container; pour the pickling liquid over the eggs, then spoon the onions on top. (The onions should hold the eggs under the liquid.) Cover and refrigerate for 24 hours.
4. Remove the eggs and onions from the pickling liquid. Refrigerate in an airtight container. Serve the onions (which are also delicious on burgers) alongside the eggs, if desired.

Yield: 6 servings