Heat 2 tablespoons of oil in a large, heavy-bottomed frying pan or kadai over medium heat. Add the potato wedges and cauliflower florets. Fry for 8 minutes, turning occasionally, until the edges are lightly browned but the vegetables are not fully cooked. Transfer to a bowl and set aside.

In the same pan, heat the remaining 1 tablespoon of oil over medium heat. Add the cumin seeds and asafoetida (if using). Let the cumin seeds sizzle and turn fragrant, which takes about 30 seconds.

Add the finely chopped onion. Cook for 3 minutes, stirring frequently, until they become translucent and turn light golden at the edges. Add the ginger, garlic, and slit green chilies, then cook for another 1 minute until fragrant.

Stir in the chopped tomatoes, turmeric powder, Kashmiri red chili powder, coriander powder, cumin powder, and salt. Cook for 4 minutes, mashing the tomatoes with your spatula, until they soften completely and the oil starts to separate from the sides of the paste.

Gently add the seared potatoes and cauliflower back into the pan. Fold them carefully into the tomato-spice mixture until evenly coated. Cover the pan with a tight-fitting lid, lower the heat to low, and cook for 12 minutes. Stir once halfway through, very gently, to prevent sticking.

Remove the lid. Sprinkle the garam masala, amchur, crushed kasuri methi, and chopped fresh coriander over the top. Toss gently on low heat for 1 minute and 30 seconds to blend the finishing flavors without breaking the vegetables. Turn off the heat and serve.