6 cloves garlic, finely grated
4 teaspoons fresh ginger, finely grated
4 teaspoons ground turmeric
2 teaspoons garam masala
2 teaspoons ground coriander
2 teaspoons ground cumin
1 ½ cups whole milk yogurt (not Greek)
1 tablespoon kosher salt
2 pounds skinless, boneless chicken breasts, halved lengthwise
3 tablespoons ghee (clarified butter) or vegetable oil
1 small onion, thinly sliced
¼ cup tomato paste
6 cardamom pods, crushed
½ teaspoon crushed red pepper flakes
1 (28-oz) can whole peeled tomatoes
¾ cup chopped fresh cilantro, plus sprigs for garnish
Steamed basmati rice for serving
2 cups heavy cream
Combine garlic, ginger, turmeric, garam masala, coriander and cumin in a small bowl.
Whisk yogurt, salt, and half the 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 pepper flakes 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 on bottom of pot, until sauce thickens, 8-10 minutes.
Add cream and chopped cilantro. Simmer, stirring occasionally, until sauce thickens, 30-40 minutes.
Meanwhile, heat broiler. Line a rimmed baking sheet with foil and set a wire rack inside the 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.
Add ½ teaspoon crushed red pepper flakes. Cut chicken into bite-size pieces, add to sauce, and simmer, stirring occasionally, until chicken is cooked through, 8-10 minutes. Serve with rice and cilantro sprigs.
Chicken can be made 2 days ahead. Cover; chill. Reheat before serving.