In a slow cooker mix the coconut milk with ginger and green curry paste and fish sauce. Add chicken and onions and cover and cook on low heat for 2.5 hours until chicken is tender. Add potato and tomato and cook on low for 1 hour until potatoes are tender.

Transfer chicken and vegetables to shallow bowls. Skin fat from surface and transfer sauce to blender. Add lime juice and remaining green curry paste and fish sauce. Purée until smooth. Season with salt and pepper and pour over chicken. Sprinkle with cilantro leaves and serve with rice.