Heat the oil in a pot or Dutch oven over medium heat. Add onion, garlic & ginger & cook, stirring occasionally, for 5 minutes or until softened.
Add curry powder, turmeric & cayenne pepper. Cook for 1 minute or until fragrant.
Add carrot, sweet potato, broth, coconut milk, salt & pepper. Bring to a boil, then reduce to a simmer. Add chicken. Cover & cook for 25 minutes, stirring occasionally, until chicken is tender & veggies are cooked.
Remove chicken from the pot & using two forks, shred chicken into small pieces. Return chicken to pot with spinach & cilantro. Cover & cook for about 2 minutes or until spinach is just wilted.
Ladle into warm bowls & serve with pappadums or toast.