Place the split peas in a bowl and cover with hot water.
Let them soak for 1 hour, then drain completely.
While they soak, sort, wash, and drain the split moong or toovar dal.
Combine the drained split peas, washed dal, rice, butter or ghee, turmeric, asafetida, green chili, ginger, carrots, cauliflower, radishes, and water in a 6-quart/liter pressure cooker. Lock the lid and cook under high pressure for 20-22 minutes.
Remove the cooker from the heat and allow the pressure to drop naturally.
Once safe, open the lid. Carefully transfer the soup in two batches to a blender, blending each batch on high speed until completely smooth and creamy.
Pour the blended soup into a large saucepan.
Stir in the ground coriander, cumin, and garam masala.
Bring the soup to a gentle boil over medium heat, stirring occasionally, and cook for 1-2 minutes to allow the flavors to meld.
Remove the pan from the heat.
Stir in the black pepper, salt, and fresh minced parsley or coriander.
Taste and adjust seasoning if necessary, then serve hot.