Heat oil in a small frying pan over high heat. Add mustard seeds and let most of them pop, about 2 minutes. Add turmeric and asafetida, swirling pan to coat. Carefully add curry leaves, watching for splattering. Remove from heat and set aside.
Blend remaining ingredients in a food processor until smooth, adding up to 1/4 cup of water if it looks too thick.
Transfer to a serving bowl and stir in spiced oil mixture.
*Find in Indian grocery stores. You can use 4 or 5 dried curry leaves instead of fresh (don't use powder). If you can't find asafetida and curry leaves, relish won't have the same Indian flavor, but will still taste fresh and delicious.
Make ahead: Up to 2 days. Cover and chill.