Heat oil in a large saucepan on medium-high heat. Add curry powder, turmeric, paprika, and allspice. Cook until fragrant, stirring constantly, about one minute.
Add the onion, garlic, ginger, bell pepper, and thyme and cook, stirring, until the onion is soft, about 2 minutes.
Stir in cubed turnip and stir to coat. Add vegetable broth, andScotch bonnet pepper, cover, and bring to a boil.
Reduce to a simmer and cook turnip until tender, about 20-25 minutes, or until there is a thick sauce. Add salt to taste.