Bring a large pot of water to boil. Add dried udon and cook for approximately 12 minutes. Drain noodles in a metal strainer and rinse with cold water. Divide into 4 bowls.
Bring chicken broth to a boil. Add chicken breast and cook for 10 minutes over medium heat. Remove chicken breast with tongs. When cool enough to handle, shred the meat. Divide into 4 portions and place on top of noodles in each bowl.
Add sliced mushroom and fish sauce to the chicken broth. Season with salt and pepper. Allow soup to simmer on low heat for 5 minutes. Turn off heat.
Place a handful of baby spinach on top of noodles in each bowl.
Immediately ladle boiling broth and mushrooms into each bowl. Garnish with sliced green onions and fried shallots. Drizzle with a few drops of sesame oil.