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 4-6 hours. Cover and chill remaining spice mixture.
Heat ghee in a large, heavy pot over medium heat. Add onion, tomato paste, cardamom, 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, approximately 4 minutes.
Add tomatoes with juice, mashing them with your hands as you add them. Bring mixture to a boil, then 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 gently, stirring occasionally, until sauce thickens, 30-40 minutes.
Meanwhile, preheat broiler. Line a rimmed baking sheet with foil and set a wire rack inside sheet. 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.
Cut chicken into bite-size pieces and add to the sauce, and simmer, stirring occasionally, until chicken is cooked through, 10-12 minutes. Top with chopped cilantro and serve with cooked Basmati rice and warm Nan (bread).
