In a large pot, bring 10 cups water to a boil.
Add chicken, onion, garlic, parsley, cilantro, celery, and bay leaves.
Cook 30–40 minutes until chicken is tender.
Remove chicken and shred into medium chunks. Reserve cooking broth.
Add bell pepper, tomatoes, and dried chiles to broth.
Simmer 10–15 minutes until soft.
Transfer vegetables and chiles to a blender with 6 cups broth, sesame seeds, pepitas, sugar, bouillon, oregano, and chili powder.
Blend until smooth.
Heat oil in the same pot.
Pour in blended sauce and stir in shredded chicken.
Add Worcestershire, tomato paste, salt, and pepper.
Simmer 30 minutes until thickened.
Slice bolillos and spread mayonnaise.
Layer with lettuce, watercress, tomato, cucumber, and radish.
Top generously with saucy chicken, adding extra sauce over the filling.
Serve warm and enjoy.