For stock, place veal in a 6- or 8-quart Dutch oven or stockpot. Cut onions into wedges. Add onions, mushrooms, leeks, peppercorns, bay leaves, fennel, and salt to veal. Add wine and water. Bring to boiling. Reduce heat. Simmer, covered, for 2 hours. Lift out meat bones with a slotted spoon; set aside.
Separate the egg, reserving the shell. Crush the shell. Save the yolk for another use. In the Dutch oven stir together the strained broth, 1/4 cup cold water, egg white, and shell. Bring to boiling. Remove from the heat and let stand for 5 minutes. Strain the stock again through a large colander or sieve lined with several layers of damp cheesecloth.
Remove fat. If desired, when bones are cool, remove meat and reserve for another use. Discard bones. Store stock and meat in separate covered containers in the refrigerator for up to 3 days or in the freezer for up to 6 months. Label type of stock, quantity, and date.