Place dried coconut in a little hot water to plump it up.
Put the oil in a tempering pot or a little pan over medium heat. When the oil is hot and shimmering, add one black mustard seed. When the seed sizzles and pops, add the rest of the mustard seeds and the asafetida. Keep a lid handy to cover the pan while the mustard seeds are popping. When the popping starts to subside (a few seconds), turn the heat to medium-low. Rub the curry leaves between your fingers a little to release their natural oils, and drop them and the green chile into the oil. Cover immediately, as moisture from the curry leaves will cause the oil to spatter. Then stir to evenly coat everything with oil and continue to fry until the chile is less raw, 10 to 15 seconds.
Add the shredded beet, turmeric powder, 1⁄4 teaspoon of salt and a few tablespoons of water to the pan. Mix well and stir-fry over medium heat until tender and cooked through, 8 to 10 minutes. Add a touch more water to the pan if it looks dry. Transfer the beets to a medium bowl to cool. (To speed up the process, you can put the bowl in the freezer.)
When the beets have cooled, combine them with the beaten yogurt, coconut and chopped cilantro. Add the remaining 1⁄4 teaspoon salt. Garnish with chopped cilantro and serve.