Combine cold water and chicken parts in a large pot.

Add ginger, leeks, salt, and pepper to the pot.

Bring to a boil, then reduce heat and simmer for 30-45 minutes, partially covered, skimming off any froth.

Line a colander with cheesecloth and strain the broth into a bowl.

Discard solids and return the strained broth to the pot.

Bring broth to a boil and swirl in beaten egg whites to create egg ribbons.

Remove from heat and strain again through a cheesecloth-lined colander.

Cook udon noodles in boiling water until done.

Rinse the cooked noodles.

Place noodles, radishes, scallions, and cabbage in individual soup bowls.

Ladle hot broth over the vegetables and serve immediately.