Heat the oil in a large saucepan over medium-high heat. Add the onion and sweet potato; cook and stir for 3 to 4 minutes or until onion has softened. Add the chicken and cook for 5 minutes or until lightly browned.
Stir in curry paste and cook for 1 minute or until fragrant. Add the tomatoes; bring to the boil and reduce heat to low. Simmer, covered, for 10 minutes.
Stir in cream and cook over very low heat, uncovered, for 8-10 minutes or until chicken and sweet potato are cooked through. Stir in spinach leaves and half the coriander.
Serve curry with brown rice, topped with yoghurt and remaining coriander.