Combine the chicken breast with 2 & 1/2 cups of water in a medium saucepan.
Season with salt, cover with a lid, and bring to a boil.
Simmer until the meat is cooked --- and do not throw the water away after cooking.
Combine the achuete seeds with a 1/4 cup of hot water, then set aside.
Place the sotanghon noodles in a bowl of room-temperature water. (NOTE: Ensure the noodles are fully submerged to soften them.) Once the chicken is cool enough to handle, use your hands to pull the meat from the skin and bones --- try to keep them almost the same size as the vegetables.
Use your fingers to rub the achuete seeds together, turning their water into orange-reddish color, then set it aside.
Place a wok (or skillet) over medium-high heat.
Add and heat the oil.
Once the oil is ready, add garlic, onion, and sauté until they soften.
Add the chopped carrot and celery and cook for a couple of minutes.
Add the meat, chopped mushrooms, and snap peas, then combine.
Use a strainer to pour the achuete water into the wok.
Add 3/4 cup of the water from cooking the meat earlier.
Cover with a lid and bring to a quick boil.
Use a colander or strainer to drain the sotanghon.
Uncover the wok, taste, and season with fish sauce and pepper.
Add the drained sotanghon and mix to combine everything evenly --- keep mixing until the noodles are cooked.
Transfer your pancit sotanghon guisado into plates and garnish with chopped green onions, if desired.
Serve with calamansi or lemon slices --- enjoy!