Heat the oil in a large saucepan over medium-high heat. Cook the onion and kumara, stirring, for 3-4 minutes or until onion is soft. Add the chicken and cook, stirring, for 5 minutes or until lightly browned.
Add the curry paste and cook, stirring, for 1 minute or until fragrant. Add the tomatoes. Bring to the boil and reduce heat to low. Simmer, covered, for 10 minutes.
Add the cream and simmer, uncovered, for 8-10 minutes or until chicken and kumara are cooked. Stir in the spinach and half the coriander. Serve curry topped with yoghurt and remaining coriander.