Coat the sweet potatoes with 1 tablespoon of the peanut oil and place in an oven-proof pie tin. Place the pie tin in the oven and roast the sweet potatoes for 50 minutes to 1 hour, or until the potatoes are fully roasted and fork tender. Once the potatoes are cool enough to handle, remove the skin from the potatoes and discard them. Reserve the sweet potato flesh until ready to use.
Place the tomatoes in a small mixing bowl and coat with 1 tablespoon of peanut oil. Lay the tomatoes on a baking sheet, skin side up, and season with salt and pepper. Place the sheet pan in the oven and roast the tomatoes until the skins are caramelized and wilted, about 25 to 30 minutes. Remove the tomatoes from the oven, discard the skins, and set the tomatoes aside until ready to use.
Set a 1 gallon stockpot over a medium high heat and add 2 tablespoons of peanut oil. Add the curry powder to the pot and toast for about 30 to 45 seconds, stirring constantly. Add the onions and saute for 3 to 4 minutes. Add the minced garlic to the pot and cook, stirring, for 30 seconds. Add the cayenne pepper and chicken stock to the pot and bring to a boil. Reduce the heat to a simmer.
Add the roasted sweet potatoes and tomatoes to the soup. Add the peanut butter and coconut milk to the pot and stir to blend. Let simmer for 10 minutes, and blend with an immersion blender or in batches in a bar blender until smooth. Season with 3/4 teaspoon of the salt and, if necessary, more pepper.
Season the chicken pieces with the remaining teaspoon of salt and the white pepper, and sear in a hot saute pan with the remaining 1 tablespoon of peanut oil for 5 minutes. Add the seared chicken to the pot. Cook until the chicken is tender, about 10 to 15 minutes.
To serve, ladle the soup into bowls and garnish with extra cilantro and the chopped peanuts.