After cooking the dal, remove the cooked dal without removing any of the cooking liquid from the pot; you will be working with the liquid - not the dal. Reserve the cooked dal for another use, such as a traditional Indian 'dal' or any other curry.
To the cooking liquid in the pot, add the peppercorns, tomatoes, coriander powder, and cumin powder. Cook for 4-5 minutes over medium heat.
Meanwhile, in a separate pan, dry-roast mustard seeds until they pop. Add asafoetida and curry leaves, and mix well. Add this mixture to the rasam liquid (the liquid in the pot).
Continue cooking the soup for about 15 more minutes, until the soup is flavorful but still thin in consistency. Sprinkle a pinch of salt and pepper, as desired.
Garnish with coriander leaves or parsley, and serve hot.