Wash and soak the toor dal for atleast 15 minutes and pressure cook it. Once cool, mash it well and keep aside.
Roughly chop the tomatoes and keep aside.
Soak marble size tamarind ball in hot water for atleast 10 minutes. Extract pulp or juice and keep aside.
In a small tempering pan, dry roast black peppercorns and jeera or cumin seeds until they are warm and aromatic. Do not over roast.
Cool this and grind it coarsely either in a mixer grinder jar or a mortar pestle.
Heat a thick bottom steel pan, add the tamarind pulp or extract, chopped tomatoes along with some curry leaves (roughly torn) and some water to cook (approximately 2 cups).
To the above, add turmeric powder and some hing. Allow the tamarind broth to reduce in quantity and the tomatoes to turn slightly mushy. There should be no raw tamarind smell.
Add the cooked and mashed lentils or dal and coarsely ground pepper + cumin powder along with salt to taste.
Now add the finely chopped coriander leaves and 1/2 tsp Jaggery and mix well. At this point adjust the consistency of your rasam by adding some water. Once you add water, remember to adjust salt.
Add the pudina or mint leaves and reduce the flame. Gently allow the rasam to froth and once it does, switch off the gas flame immediately.
For the tempering, heat a pan, add ghee or clarified butter, jeera and mustard seeds. Once mustard crackles, add a pinch of hing and curry leaves. Pour this tempering over the piping hot rasam and cover it immediately.
Allow the rasam to absorb all the flavors. Serve after 5 to 7 minutes with steamed rice and a poriyal of your choice.