In a Dutch oven or similar large, sturdy pot, heat the oil over medium-high heat. Add the chicken, ½ teaspoon of the kosher salt, black pepper, and ½ tablespoon of the curry powder, stirring to coat the chicken evenly. Sear the chicken on all sides until lightly golden (about 5-6 minutes)—the chicken does not need to be cooked through at this point. Remove to a plate.

Reduce the heat to medium. Add 2 tablespoons of the butter and the onion to the pot. Cook until the onion is beginning to soften, about 5 minutes.

Add the garlic, ginger, garam masala, chili powder, cumin, and the remaining ¾ teaspoon salt and 1 tablespoon curry powder. Stir and cook until fragrant, about 30 seconds.

Reduce the heat to low. Carefully pour in the tomato sauce (be careful of splatters). Fill the can of tomato sauce up halfway with water, then add the liquid to the pot. Stir to combine, then partially cover the pot and let simmer gently for 15 minutes.

Return the chicken and any juices that have collected on the plate to the pot. Stir in the half-and-half. Let simmer until the chicken is fully cooked through, about 5 minutes more.

Place the Greek yogurt in a small bowl and add a few big spoonfuls of the hot butter chicken liquid. Stir to combine, then add the mixture to the pot (this tempers the yogurt so it doesn't curdle).

Stir in the cilantro and 1 tablespoon butter. Enjoy warm over brown rice, quinoa, or naan, sprinkled with more cilantro.