Using a mortar and pestle, grind the cumin seeds, peppercorns, and garlic into a rough paste. Transfer the paste into a bowl and set to the side.
Place the chopped tomatoes into a large bowl and, using a hand held mixer, process the tomatoes until they are a smooth sauce. Set the sauce to the side.
In a saucepan over medium heat, heat the oil, then add the mustard seeds. Heat the mustard seeds for 30 seconds, then add the hing, the halved kashmiri chili, and the curry leaves. Stir to combine.
Add the cumin/peppercorn/garlic paste and continue to cook the mix, stirring often, for 30 seconds to one minute.
Add the tomato sauce and stir well. Cook the mix for 30 minutes over medium-low heat, stirring often.
Add the kashmiri powder, 1/2 of the coriander leaves, salt, and the diced tomatoes. Stir well, then allow the soup to simmer for a minute or two (stirring occasionally).
Add the water, then bring the soup to a quick boil. Once boiling, reduce the heat to low and allow the soup to simmer 5 minutes.
Remove the soup from the heat and add the remaining coriander leaves. Stir to combine.
For extra spiciness, you can sub-in homemade rasam powder (store-bought or homemade) in the making of the cumin, black peppercorn, and garlic paste. Replace the cumin and black peppercorn with a tablespoon of rasam powder (it contains those ingredients plus others, and it adds extra spiciness).Or, if you prefer a more spice-potent tomato rasam, keep the cumin/black peppercorn paste step in place and simply add in an additional teaspoon of rasam powder as a last step in the recipe.