Add the coconut, green chilies, ginger, salt, and water to a blender and grind to a smooth paste. Transfer to a bowl.
For the tempering, heat the oil in a small pan over medium heat. Add the mustard seeds and let them pop, then add the hing.
Add the urad dal and dried red chilies and stir for about 30 seconds, until the dal begins to change color. Add the curry leaves, stir, and remove from the heat.
Pour the tempering over the chutney, stir, and serve.