Cook the dal with turmeric in a pressure cooker or on the stovetop with 2 cups of water until it's really soft. Use a whisk to mash the dal up. Do not discard the stock.
Using a mortar and pestle, or in a food processor, crush 2 cloves of garlic, the green chili pepper, and cumin seeds to a coarse paste.
Crush the remaining garlic cloves slightly but let them hold their shape.
Heat the oil in a saucepan.
Add the mustard seeds and, when it sputters, add the asafetida.
Add the cumin-garlic-chili paste, stir-fry for a few seconds, then add the ginger, curry leaves, coriander leaves, and crushed, whole garlic. Stir-fry for a few seconds until the garlic starts to very slightly change color.
Add the tomatoes and stir-fry until they just start to turn mushy.
Add the tamarind extract with 1 cup of water and bring to a boil. Add the rasam powder and continue to boil for another five minutes.
Add the cooked dal/lentils to the saucepan with salt to taste. Bring the rasam to a rolling boil, reduce heat to medium, and let it boil for another five minutes. If it starts to get thick, add water. Rasam should have a very watery consistency, although if you prefer it thick, you can add less water.
Check salt and add more if needed.
Serve very hot over rice or in a glass or bowl.