In a large bowl, vigorously whisk 240g room-temperature sour yogurt with 35g gram flour (besan) until absolutely smooth with no lumps. Gradually whisk in 720ml of water along with the turmeric and red chili powder until it resembles a thin, uniform yellow milk.
Pour the mixture into a deep, heavy-bottomed pot. Turn the heat to medium and stir continuously in one direction until the mixture comes to a full, bubbling boil. Once boiling, turn the heat to low and let it simmer gently for 25-30 minutes, stirring occasionally, until it thickens slightly and the raw taste of the flour is entirely gone.
While the gravy simmers, place 150g sliced onions in a bowl and sprinkle with 1/2 tsp salt. Squeeze them with your hands for a minute to release their natural moisture. Add 100g besan, carom seeds, chopped green chili, and a splash of water (about 2-3 tablespoons) to form a very thick, sticky batter that heavily coats the onions.
Heat oil in a deep frying pan over medium heat. Drop small, spoonfuls of the onion batter into the hot oil. Fry until they are deep golden-brown and crispy on the outside, about 4-5 minutes. Drain on paper towels and set aside.
Gently drop the fried pakoras into the simmering yogurt gravy. Let them simmer together on very low heat for 5-10 minutes so the pakoras absorb the flavors and soften slightly.
In a small pan, heat 2 tbsp of ghee. Add cumin seeds, fenugreek seeds, and dry red chilies. Let them sizzle and turn fragrant for 30 seconds. Turn off the heat, stir in the Kashmiri red chili powder, and immediately pour this sizzling mixture over the hot Kadhi. Serve immediately.