Begin by cleaning the chicken pieces with lime juice and water to remove any impurities. Rinse thoroughly and pat dry with paper towels.

In a large stockpot, combine the cleaned chicken, chopped onion, minced garlic, scallions, thyme, and allspice berries. Pour in the water or chicken broth, ensuring the chicken is fully submerged. Bring to a boil over medium-high heat, then reduce to a simmer. Cook for about 20 minutes, skimming off any foam that rises to the surface.

Add the diced pumpkin, carrots, chayote, and yellow yam to the pot. If using green bananas, add them now as well. These root vegetables contribute to the soup's hearty texture and flavor. Continue to simmer for another 20 minutes, or until the vegetables are tender.

Add the egg noodles or broken spaghetti to the pot. If you prefer a spicier soup, carefully place the whole scotch bonnet pepper into the broth, ensuring it remains intact to control the heat level. Be cautious not to burst the pepper unless you desire more heat.

Season the soup with salt and freshly ground black pepper to taste. If using a chicken noodle soup mix, stir it in now for enhanced flavor. Let the soup simmer for an additional 10-15 minutes, or until the noodles are cooked al dente. Remove the scotch bonnet pepper before serving.