Blend all curry paste ingredients in a food processor until smooth.
Cook the paste in a frying pan over medium heat for 3 minutes until fragrant.
Season the chicken thighs thoroughly with black pepper.
Add chicken, cinnamon, and star anise to the pan and cook until pale golden-brown.
Add 100ml of water, boil, then transfer to a slow cooker with potatoes and carrots.
Whisk cornflour with 2 tablespoons of water, stir in coconut milk, and add to the cooker.
Cover and cook on high for 3 hours, stirring in green beans at the very end.
Serve the curry plain or accompanied by steamed rice.