1. In a large bowl, whisk together the yogurt, lemon juice, 1 teaspoon of the salt, turmeric, and 1 teaspoon of the Kashmiri chili powder. Add the chicken pieces, toss to coat well, cover, and marinate in the refrigerator for at least 30 minutes or up to overnight.

2. Heat 2 tablespoons of the ghee or oil in a wide heavy pan over medium-high heat. Shake excess marinade from the chicken pieces and sear them in batches until lightly browned on the outside. Transfer browned chicken to a plate; it does not need to be cooked through yet.

3. Reduce the heat to medium and add the remaining tablespoon of ghee or oil to the pan if needed. Add the sliced onions and cook, stirring often, until they become very soft and deeply golden brown, 10 to 15 minutes.

4. Stir in the garlic and ginger and cook until fragrant, about 1 minute. Add the tomato paste and cook, stirring, until it darkens slightly and smells sweet. Sprinkle in the remaining 1 teaspoon Kashmiri chili powder, cumin, coriander, cardamom, cinnamon, and black pepper, and toast the spices for another minute.

5. Pour in the tomato puree and chicken stock, stirring to combine into a smooth sauce. Add the remaining 1/2 teaspoon salt and the sugar, if using. Bring the mixture to a gentle simmer.

6. Return the seared chicken and any accumulated juices to the pan, nestling the pieces into the sauce. Cover and simmer over medium-low heat for 20 to 25 minutes, stirring occasionally, until the chicken is cooked through and very tender and the sauce has thickened.

7. Stir in the garam masala and simmer uncovered for 3 to 5 minutes more so the flavors meld. Add the heavy cream or coconut milk, if using, and heat just until the sauce is silky but not boiling.

8. Taste and adjust seasoning with more salt or chili to taste. Sprinkle with chopped cilantro and serve hot over basmati rice or with warm naan.