Heat a large pot on medium heat for 2 minutes. Put the leeks, red and yellow onions, leeks, celery, shallots, and garlic in the pot. Cook, stirring occasionally, until the vegetables start to brown and stick to the bottom of the pot, about 5 minutes. Stir in 2 tablespoons of the broth and use the spoon to loosen any bits that are stuck to the bottom of the pot. Continue browning the vegetables for 5 minutes, stirring frequently. Stir in 2 more tablespoons of broth and once again loosen any bits that are stuck to the pot. Continue to brown the vegetables and add broth in this fashion, decreasing the heat a bit each time; the more often you repeat these steps, the richer the flavor of the soup will be. Continue until the onions turn a deep brown but are not burnt. Stir in the vinegar and use the spoon to loosen any bits that are stuck to the pot. Stir in the remaining broth and increase the heat to high. Bring to a boil, decrease the heat to medium-low, and simmer uncovered for 20 minutes, stirring occasionally. Serve hot, garnished with the chives.