Combine garlic, ginger, turmeric, garam masala, tikka masala paste, 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 let marinade for at least 1 hour to overnight.
Heat vegetable or clarified butter in a large heavy pot over medium heat. Add onion, tomato paste, tikka masala paste, cardamom, and chiles and cook, stirring often, until paste has darkened and onion is soft. 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, about 25 minutes. Season to taste.
Meanwhile, preheat broiler/oven to 425 degrees F. 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), 7 to 10 minutes.
Cut chicken into bite-size pieces, add to sauce, and simmer, stirring occasionally, until chicken is cooked through, 8 to 10 minutes. Serve with rice and chopped cilantro.
Combine garlic, ginger, turmeric, garam masala, tikka masala paste, 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 let marinade for at least 1 hour to overnight.
Heat vegetable or clarified butter in a large heavy pot over medium heat. Add onion, tomato paste, tikka masala paste, cardamom, and chiles and cook, stirring often, until paste has darkened and onion is soft. 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, about 25 minutes. Season to taste.
Meanwhile, preheat broiler/oven to 425 degrees F. 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), 7 to 10 minutes.
Cut chicken into bite-size pieces, add to sauce, and simmer, stirring occasionally, until chicken is cooked through, 8 to 10 minutes. Serve with rice and chopped cilantro.