In the bowl of a food processor, combine the ground meat with the onions, leeks, celery, carrots, thyme, tarragon, parsley, garlic, and black pepper. Puree on high speed.
In a bowl, combine the egg whites with the pureed meat mixture. Stir well to blend.
Place the stock in a large pot and add the "raft" (the pureed meat-egg white mixture). Bring to a boil, stirring constantly to prevent the raft from sticking to the bottom and sides of the pot. (Once the stock has come to a boil, do not stir again.) Reduce to a simmer and puncture a hole in the center of the raft for the stock to circulate through and clarify. Simmer for 15 minutes. Remove from the heat. Gently poke a hole in the raft large enough to fit a ladle. With a ladle, gently scoop out the consomme into a clean pot or bowl. Strain through a layer of cheesecloth to finish clarifying.
Serve hot with desired garnish. Alternatively, transfer consomme to a shallow bowl or roasting pan and cool to room temperature. Refrigerate until thoroughly chilled, covering with plastic wrap only when the consomme is cool enough that no condensation forms on the plastic. When the consomme is completely cooled, cut it into 1/2-inch cubes and divide between consomme cups. Garnish with sour cream, chopped chives, and a lemon slice and serve with toast points.