2 onions, sliced
2 cups balsamic vinegar 4 cups water
4 tablespoons white sugar
20 cloves garlic, mashed into a paste
1/2 cup beet juice (see Cook’s Note)
6 fresh green and red cayenne chiles, halved lengthwise
Place the eggs into a large pot cover with water by 1 inch. Cover the saucepan and bring the water to a boil over high heat; remove from the heat and let the eggs stand in the hot water for 15 minutes. Pour out the hot water and cool completely under cold running water; peel and place in a glass jar large enough to hold them.
Combine the onions, balsamic vinegar, water, sugar, garlic, peppercorns, beet juice, and cayenne chiles in a deep saucepan over high heat; bring to a boil and immediately remove from heat. Allow the mixture to cool to room temperature. Pour into the glass jar with the eggs. Seal the jar with the lid. Refrigerate 4 to 5 days before serving.