In a blender or food processor, combine the freshly grated coconut, roasted sesame seeds, green chillies, ginger, yogurt, and salt. Add water as needed to achieve the desired consistency.
Blend the mixture until it is smooth and creamy. Taste the chutney and adjust the salt and spiciness to your liking.
In a small pan, heat the oil over medium-high heat. Add the mustard seeds and asafoetida and fry until the mustard seeds begin to pop.
Add the curry leaves to the pan and fry for a few seconds until they are fragrant.
Pour the tempering over the coconut chutney and mix well.
Serve the coconut chutney with dosa, idli, or any other South Indian dish of your choice.