Grate the beets with their skins on. Add the grated beets to a pan and season with salt. Add a touch of water (about 1 tbsp) and cook covered until they are tender.
Check occasionally and add more water if they start to stick to the bottom. Pinch a piece between your fingers and taste to check that they are done. Add to a bowl.
Grind the coconut and green chillies to a fine paste. Add to the cooked beets.
Tempering: heat the oil in a small pan and add the mustard seeds. Once they start to pop, add the cumin seeds, urad dhal, dried chillies and curry leaves. The urad dhal will start to brown in about 15 seconds. Add the chopped shallots at this stage and sauté until browned around the edges.
Tip the tempered spices into the bowl with the beets and ground coconut. Toss it all together with the yogurt. Check for seasoning and add more salt if necessary.
If the yogurt is too thick, add a bit of water to loosen.