Add olive oil to a large pot over medium high heat. When hot, add the onion, carrots, celery, garlic, and ginger, and saute until onions are soft and translucent.
Pour chicken broth into the pot, bring to a boil, and then turn down to a simmer. Add soy sauce, chili pepper flakes to taste, and mushrooms. Cook on low heat with the lid on for at least 20 minutes.
When the chicken is done roasting, add a few spoonfuls of chicken drippings to the pot. When the chicken is cool enough to touch, tear chunks of meat off and add to the pot, along with the udon noodles. Let stew on low for at least 5 more minutes.
When ready to serve, stir in chop scallions. Ladle into bowls, and sprinkle sesame seeds on top to garnish. If you wish, add sriracha sauce to taste.