In a large mixing bowl, combine the chicken pieces with all marinade ingredients (yogurt, ginger-garlic paste, red chili powder, garam masala, turmeric, salt, lemon juice, oil). Mix well to coat the chicken evenly.

Cover the bowl and refrigerate for at least 30 minutes, or preferably 2-4 hours, or even overnight for best results.

Heat a heavy-bottomed skillet or grill pan over medium-high heat. Add 1 tablespoon of oil if not using a non-stick pan.

Once hot, add the marinated chicken pieces in a single layer, without overcrowding the pan. Cook in batches if necessary.

Sear the chicken for 3-4 minutes per side until lightly charred and cooked through. Remove the cooked chicken and set aside. (The charring adds a smoky flavor similar to tandoor cooking).

In a large heavy-bottomed pot or Dutch oven, melt 4 tablespoons of unsalted butter over medium heat. Add the finely chopped yellow onion and sauté until softened and translucent, about 5-7 minutes.

Add the ginger-garlic paste and green chili (if using) and sauté for another 1-2 minutes until fragrant.

Stir in the red chili powder, garam masala, ground cumin, ground coriander, and turmeric powder. Cook for 30 seconds, stirring constantly, to bloom the spices.

Pour in the crushed tomatoes, water (or broth), and tomato paste. Add sugar and salt. Bring the mixture to a simmer.

Reduce the heat to low, cover the pot, and let the sauce simmer for 15-20 minutes, stirring occasionally, allowing the flavors to meld and the sauce to thicken slightly.

Carefully transfer the hot sauce to a blender (or use an immersion blender directly in the pot) and blend until completely smooth. Strain the sauce through a fine-mesh sieve back into the pot for an ultra-smooth consistency, pressing solids to extract all liquid. (This step is optional but highly recommended for restaurant-style smoothness).

Return the pot to low heat. Stir in the cooked chicken pieces and the heavy cream.

Add the crushed kasuri methi (dried fenugreek leaves), if using. Simmer gently for another 5-7 minutes, allowing the chicken to warm through and absorb the sauce flavors. Do not boil after adding cream.

If desired, heat a small piece of charcoal directly on an open flame or stovetop burner until it's glowing red.

Place a small heat-proof bowl or a piece of foil in the center of the butter chicken. Place the hot charcoal in the bowl/foil.

Drizzle 1 teaspoon of ghee or butter over the charcoal. Immediately cover the pot with a tight-fitting lid to trap the smoke. Let it infuse for 5-10 minutes. Discard the charcoal before serving.

Garnish with fresh chopped cilantro. Serve hot with basmati rice, naan bread, or roti.