In a pot over medium heat, combine chicken and water. Bring to a boil, skimming scum that floats on top.
When broth clears, add quartered onions, crushed garlic, ginger, bay leaf, peppercorns, and about 1 tablespoon salt. Lower heat, cover, and simmer for about 20 to 30 minutes or until chicken is cooked through.
With a slotted spoon, remove chicken and allow to cool. Shred chicken meat and return bones to the pot. Continue to simmer broth for about 10 to 15 minutes or until reduced to about 2 to 3 cups.
Using a fine-mesh sieve, drain the broth, and discard bones and aromatics.
In a bowl, combine black fungus and enough warm water to cover. Soak for about 30 minutes or until softened. Drain from water and with hands, squeeze excess liquid. With a knife, slice into very thin strips. Set aside.
In a wide skillet or wok over medium heat, heat oil. Add snow peas and cook, stirring regularly, for about 10 seconds. Remove from pan and drain on paper towels.
Add onions and garlic and cook until softened.
Add mushrooms and cook for about 1 minute.
Add celery and carrots and cook, stirring regularly, for about 1 to 2 minutes or until half-done.
Add fish sauce and cook for another minute.
Remove vegetable mixture from the pan and keep warm.
Add broth to the pan and bring to a boil.
Add atsuete powder and stir until well dispersed. Season with salt and pepper to taste.
Add sotanghon noodles and using tongs, toss in the broth to loosen.
Continue to toss for about 3 to 5 minutes or until noodles are cooked through but firm to bite. Add more of the reserved if needed.
Add the shredded chicken and vegetable mixture, Toss to redistribute and cook until vegetables are tender-crisp and most of the liquid is absorbed.
Add snow peas. Adjust seasonings if needed.
Transfer to a serving plate and garnish with green onions and fried garlic bits. Serve hot with calamansi on the side.