Soak the chana dal and toor dal for 30 minutes or more. Drain and add to a blender with the cumin, asafetida, chilies, sambar powder and turmeric. Add salt to taste and using just enough water to keep the blades moving, blend into a smooth paste.
Remove the dal paste to a microwave-safe bowl. Microwave for 2 minutes. The paste would be cooked on top. Turn over with a spoon so the uncooked paste on the bottom is now on the top and microwave 2 more minutes.Set aside.
In a cast-iron or non-stick skillet, heat the oil.
Add the mustard seeds and cumin seeds. When they sputter, add udad dal and stir, allowing the dal to brown lightly, about 30 seconds to a minute.
Add the cabbage and some salt. Stir-fry the cabbage on medium heat until it is beginning to get tender, about 5 minutes.
Now, with your fingers, crumble the dal paste into the skillet over the cabbage.
Continue to stir-fry the cabbage until it is quite tender but has a slight bite, and the dal dumplings are a couple of shades darker.
Check salt and turn off heat.