Cook the ash gourd pieces with salt, a few curry leaves, and a little water until tender.
Grind the grated coconut, green chilies, and curd in a mixer jar. Finally, add the mustard seeds and pulse it just once (be careful not to over-grind the mustard).
Add this coconut-curd mixture to the cooked ash gourd and mix well. Check for salt and adjust if necessary.
Heat coconut oil, splutter mustard seeds, add dry red chilies and curry leaves, and pour the tempering over the pachadi. Cover it immediately to retain the flavor.