Whisk ¼ cup of chickpea flour (besan) with half of ¾ cup of plain yogurt until smooth. Whisk in the remaining yogurt and 3¼ cups of water.
Heat 1½ tablespoons of oil in a heavy pot over medium heat. Fry ½ teaspoon of cumin seeds, ¼ teaspoon of fenugreek seeds, and 1 dried red chili until fragrant, then 2 tablespoons of chopped onion and 1 chopped green chili until soft.
Stir in half of 1 tablespoon of grated ginger, ½ tablespoon of minced garlic, ¼ teaspoon of turmeric, half of ½ teaspoon of Kashmiri chili powder, ½ teaspoon of ground coriander, and ¼ teaspoon of garam masala.
Pour in the yogurt mixture and ¾ teaspoon of salt. Bring to a gentle boil over low heat, stirring, then simmer for about 30 minutes, stirring every 5-8 minutes.
Meanwhile, for the pakoras, mix ¾ cup of chickpea flour (besan), ½ teaspoon of carom seeds (ajwain), ¼ teaspoon of salt, and ⅛ teaspoon of baking soda.
Add ¾ cup of thinly sliced onion, the remaining ginger, 2 tablespoons of chopped cilantro, and 3 tablespoons of water, and mix to a thick, sticky batter.
Heat 2in / 5cm of oil in a deep pan over medium heat. Drop in small portions of the batter and leave them for 1-2 minutes, then fry, stirring, until crisp and golden. Lower the heat, fry for 1-2 minutes more, and drain.
Add the pakoras to the hot kadhi. For the tadka, heat 1½ tablespoons of ghee in a small pan and briefly fry ¼ teaspoon of cumin seeds, 2 dried red chilies, 1 sprig of chopped curry leaves, and ¼ teaspoon of asafoetida (hing).
Stir the remaining Kashmiri chili powder into the tadka and pour it over the kadhi.