Heat 1 tablespoon ghee or oil in a large skillet over medium-high heat. Add the roughly chopped half onion and both bell peppers and sauté until softened but still slightly crisp, about 4–5 minutes. Transfer to a bowl and set aside.
In the same skillet, add the remaining tablespoon of ghee or oil. Add the finely diced 1/2 onion and cook over medium heat until golden, about 5–6 minutes.
Add the chopped jalapeno (or red chili), minced garlic, and minced ginger to the skillet and cook, stirring, for 1–2 minutes until fragrant.
Stir in the ground coriander, cumin, garam masala, turmeric, ground cardamom, Kashmiri chili powder (if using), and asafoetida. Cook the spices for about 1 minute to bloom their flavors.
Add the cubed chicken to the skillet and cook, stirring occasionally, until the outside turns white but the chicken is not fully cooked, about 3–4 minutes.
Pour in the tomato puree (or crushed tomatoes) and stir in the tomato paste, bay leaf, sugar, salt, and black pepper. Bring the mixture to a low simmer.
Cover and simmer gently for 20 minutes, stirring occasionally, until the chicken is cooked through and flavors have melded.
Return the cooked onions and bell peppers to the skillet, stir to combine, and simmer uncovered for another 3–4 minutes. Adjust seasoning with additional salt and pepper if needed.
Serve the Chicken Jalfrezi with steamed rice, naan, or your preferred bread.