Cook the leeks in the butter in a saucepan over medium heat, stirring often until they begin to wilt, about three minutes. Add the broth and rice. when the soup begins to boil, cover the pot and let the soup slowly simmer at low heat for 20 minutes, or until the rice is very tender.

Stir the parsley, mint, and a few grindings of black pepper into the simmering soup and then remove it from the heat. Purée it in two batches in a blender until very smooth. Allow the blender to run at least a full minute , or until the soup is golf green and the texture is very smooth. Pour the soup back into the saucepan, stir in the cream, and reheat it. Taste it and add salt if you think it needs it.