In a large pot, combine the chicken wings or drumsticks with water. Bring to a boil over medium-high heat.
Skim off any foam that rises to the surface.
Add the finely chopped onion, minced garlic, cubed potatoes, sliced carrots, and chopped celery to the pot.
Add the whole scotch bonnet pepper (if using), allspice berries, and ground black pepper.
Reduce the heat to low and let the souse simmer for about 45 minutes, or until the chicken and vegetables are tender.
Stir in the fresh lime juice and lemon juice. Season with salt to taste.
Remove the scotch bonnet pepper and allspice berries from the pot.
Ladle the souse into bowls and garnish with freshly chopped parsley.
Enjoy your meal!