Heat some oil in a non-stick pan then add urad dal, dried red chillies, and curry leaves to it. Sauté them on medium heat for half a minute.
Add the grated beetroot, coconut, and salt to the pan and cook it for 5 minutes.
Remove the pan from the heat and let the mixture cool down completely.
Once it has cooled down, blend the mixture with 2 tablespoons of water to make a fine paste and transfer it to a bowl.
For making the tempering, heat some oil in a small pan and then add mustard seeds.
When the mustard seeds start popping, pour the warm tempering over the beetroot paste.
Serve the chutney right away or store it in an airtight container for later use.