Step 1Combine brisket, bones, ginger, peppercorns and soup stock in large pot. Add 2 1/2 quarts water. Bring to boil, then reduce heat and simmer over low heat until water reduces to about 2 quarts, 2 to 2 1/2 hours. Allow beef to cool then refrigerate; discard bones. Strain liquid through cheesecloth or very fine mesh strainer. Refrigerate beef stock 4 to 5 hours, place in freezer or cool over ice water until fat solidifies. Remove all fat from stock.
Step 2Combine rice vinegar, salt and mustard in bowl. Add to beef stock.
Step 3Cut cold beef brisket into thin 2x1-inch slices.
Step 4Bring 2 to 3 quarts water to boil in large pot and add noodles. Boil about 3 minutes. Remove noodles from heat and rinse thoroughly in cold water to cool. Drain. Place noodles in 6 to 8 large bowls.
Step 5Distribute beef stock and beef slices evenly among bowls. Add ice if desired. Garnish with cucumbers, pear slices and hard-boiled eggs. Serve immediately with Asian hot mustard, if desired.