Heat 2 tablespoons of peanut oil in a large Dutch oven or stockpot over medium-high heat. Add curry powder and cook, stirring constantly for 1 minute. Add onions and cook, stirring occasionally, for 2 minutes. Add garlic and cook for 1 more minute. Stir in sweet potatoes, chicken broth and tomatoes, and bring soup to a boil. Simmer, covered, 20 to 30 minutes.
In a large skillet, heat the remaining teaspoon of peanut oil. Add the turkey and cook, stirring with a wooden spoon to break up any clumps until cooked through. Season with 1/2 teaspoon salt and 1/4 teaspoon black pepper. Drain on paper towels.
Add cooked ground turkey, the remaining 1/2 teaspoon salt, cayenne, peanut butter, and coconut milk to the soup, stirring to combine. Bring mixture to a simmer and cook for 20 minutes.
