Soak the tamarind in 1 cup of warm water and keep aside for about 15 minutes. Then, using your fingers, rub and squeeze the softened tamarind to extract the pulp into the water. Remove the solid part of the tamarind and pour the tamarind water into a pan.
Add the vegetable pieces, salt and turmeric powder and stir a couple of times. Bring to a boil and then simmer till the vegetable is cooked. The whitish coloured vellarikkai pieces will turn translucent when cooked.
I usually do this part of the cooking in the microwave (about 7 to 8 minutes at 100%). I cook the vegetable in the tamarind water without the turmeric and salt as I find that turmeric discolours my microwave. So I add the seasoning after microwaving and on the stove-top.
In the meanwhile, grind all the ingredients for the coconut paste with a little water to a smooth paste (not watery, like you would for a chutney), and keep ready. You can leave out the curry leaves from this paste and add it to the vegetables while they cook. I add it to the paste as it lends a lot of flavour, and it doesn't have to be picked out from the pachadi while eating.
The amount of water in the cooked vegetable would have reduced to about 1/4 a cup. Now add the jaggery and the coconut paste. Mix well and let it come to a boil. Take the pachadi off the heat after a minute.
Pour the pachadi into a serving dish. Prepare the tempering by heating the oil and adding the mustard seeds. When they splutter add the lentils and stir till golden brown. Pour this into the pachadi. Stir the tempering into the pachadi just before serving.
Serve this pachadi warm, with rice and mulgootal or mulagushyam.