Heat 1 tablespoon ghee or oil in a large skillet over medium-high heat. Add the roughly chopped 1/2 large yellow 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 1 tablespoon ghee or oil. Reduce heat to medium and add the finely diced 1/2 large onion. Cook until golden, about 5 minutes.
Add the chopped jalapeño (or red chili), minced garlic, and minced ginger to the skillet and cook, stirring, for 1–2 minutes until fragrant.
Sprinkle in the ground coriander, ground cumin, garam masala, ground turmeric, ground cardamom, Kashmiri chili powder (if using), and asafoetida. Cook and stir for about 1 minute to bloom the spices.
Add the cubed 1 pound chicken to the skillet and cook, stirring occasionally, until the pieces lose their raw pink color on the outside, about 4–5 minutes.
Stir in the 15 ounce tomato puree (or crushed tomatoes), 1 tablespoon tomato paste, bay leaf, 1 1/2 teaspoons salt, 1/2 teaspoon black pepper, and 1 teaspoon sugar. Mix well and bring 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 reserved sautéed onions and bell peppers to the skillet, stir to combine, and simmer uncovered for another 3–4 minutes. Adjust salt and pepper to taste. If too dry, add a splash of water, keeping it relatively dry.
Remove the bay leaf and serve hot with steamed rice or naan.