Prepare the Mustard Base: Combine the green chilies, ginger, black mustard seeds, and peanuts in a blender. Pulse until coarsely pulverized.
Add 1 cup / 240 ml of vegetable stock, turmeric, ground coriander, jaggery, and salt. Process again until the mixture is completely smooth.
Simmer the Vegetables: Pour the remaining 3 cups / 710 ml of stock and the blended mustard mixture into a large soup pot.
Add the butter (or sesame oil), mixed vegetables, and chopped tomatoes.
Bring to a rolling boil over high heat.
Cook Until Tender: Once boiling, cover the pot and reduce the heat to moderately low.
Simmer until the vegetables are fork-tender. Note: Cut longer-cooking roots into smaller pieces and softer vegetables into larger chunks to ensure even cooking.
Prepare the Spices: While the soup simmers, combine the cumin seeds, fennel seeds, kalonji, and cassia (or bay leaf) in a small dish.
Heat the 2 tbsp / 30 ml of ghee (or oil) in a small frying pan over moderately high heat.
Fry the Tempering: When the ghee is hot but not smoking, add the spice blend.
Fry for a few seconds until the cumin and fennel seeds darken a few shades and release their aroma.
Steep the Flavor: Immediately pour the hot oil and spices into the cooked soup.
Cover the pot at once to trap the aromas and let the seasonings steep for 2 to 3 minutes.
Finish and Serve: Just before serving, uncover the pot and stir in the black pepper and lemon juice.
Transfer the soup to a warmed tureen or individual bowls and garnish generously with fresh coriander.
Don't skip the steeping step!
Pouring the hot tempering (chaunk) into the soup and immediately covering the pot traps the aromatic oils, deeply infusing the broth.