Heat your oven to 375 degrees F. Parboil the basmati rice by bringing a large pot of salted water to a boil, adding the rice, and cooking for about 8 minutes until it is just barely tender but still has a little bite in the center. Drain it well and set it aside. It will finish cooking in the oven, so do not let it get soft here.

In a small bowl, toss the chicken pieces with 1 teaspoon of the garam masala, the cumin, turmeric, salt, and pepper until evenly coated. Heat the oil in a large skillet over medium-high heat until it shimmers. Add the chicken in a single layer, working in batches if needed so you are not crowding the pan, and cook for 3 to 4 minutes per side until deeply golden brown. The chicken does not need to be fully cooked through at this point. Transfer to a plate and set aside.

Reduce the heat under the same skillet to medium. Add the diced onion and cook, stirring occasionally, for 5 to 6 minutes until softened and just starting to turn golden at the edges. Add the garlic, ginger, and tomato paste and stir constantly for 1 minute until the paste darkens slightly and smells fragrant. Add the remaining 1 teaspoon of garam masala and stir for 30 seconds more. Pour in the crushed tomatoes, chicken broth, heavy cream, and sugar. Stir everything together, scraping up any browned bits from the bottom of the pan. Let the sauce simmer for 5 minutes, then taste and adjust salt as needed.

Grease your 9x13 inch baking dish with a little oil or cooking spray. Spread the parboiled rice in an even layer across the bottom of the dish. Dot the surface of the rice with the small pieces of butter. Arrange the browned chicken pieces evenly over the rice. Pour the tomato-cream sauce over everything, making sure the chicken and rice are well covered and the sauce reaches down into the edges.

Cover the baking dish tightly with aluminum foil and bake for 25 minutes. Remove the foil and bake for another 15 to 20 minutes, until the sauce is bubbling at the edges and the surface looks slightly set and a little deeper in color. The rice on the bottom should be fully tender and have absorbed most of the sauce. If you press a spoon into the rice layer, it should feel soft with no crunch.

Let the casserole rest uncovered for 5 minutes before serving. This helps the sauce thicken slightly and makes it easier to scoop clean portions. Scatter the chopped cilantro over the top and serve with lime wedges on the side for squeezing.