Combine garlic, ginger, turmeric, garam masala, coriander, and cumin in a small bowl. Whisk yogurt, salt, and half of spice mixture in a medium bowl; add chicken and turn to coat. Cover and chill for 30 minutes, at least. Cover and chill remaining spice mixture.
Heat ghee or vegetable oil in a large heavy pot over medium heat. Add onion, tomato paste, and chiles and cook, stirring often, until tomato paste has darkened and onion is soft, about 5 minutes. Add remaining half of spice mixture and cook, stirring often, until bottom of pot begins to brown, about 4 minutes.
Add tomatoes with juices, crushing them with your hands as you add them. Bring to a boil, reduce heat, and simmer, stirring often and scraping up browned bits from bottom of pot, until sauce thickens, 8-10 minutes.
Add cream and chopped cilantro. Simmer, stirring occasionally, until sauce thickens, 30-40 minutes.
Meanwhile, preheat broiler. Line a rimmed baking sheet with foil and arrange chicken on rack in a single layer. Broil until chicken starts to blacken in spots (it will not be cooked through), about 10 minutes.
Add chicken pieces to sauce, and simmer, stirring occasionally, until chicken is cooked through, 8-10 minutes. Serve with rice and cilantro sprigs over jasmine rice!