In a small bowl, combine minced garlic, minced ginger, turmeric, garam masala, cumin, coriander, and salt. Stir well.
In another bowl, whisk together yogurt, half the spice mixture, and 2 teaspoons lemon juice. This will be your marinade to tenderize the chicken.
Halve the chicken breasts and pound them to an even thickness using a meat mallet or the bottom of a frying pan.
Add the chicken pieces to the yogurt mixture, ensuring each piece is well coated. Cover tightly or transfer to a resealable bag and refrigerate for at least 6 hours, preferably 24 hours.
While the chicken marinates, cover and chill the remaining spice mixture for later use.
In a large, heavy pan, heat vegetable oil over medium heat. Add finely chopped onion and cook until softened, about 2 to 3 minutes.
Stir in tomato paste, ground cardamom, and crushed red pepper flakes. Continue cooking, stirring frequently, until the tomato paste darkens and the onion is soft, about 5 minutes.
Add the remaining half of the spice mixture and cook, stirring often, until fragrant, about 4 minutes.
Add the fire-roasted crushed tomatoes to the mixture and bring it to a boil over high heat. Once boiling, reduce the heat and allow to simmer, stirring often until the sauce thickens, about 8 minutes.
Stir in heavy cream and cilantro. Simmer over low heat until the sauce thickens further, about 30 to 40 minutes.
Preheat a grill or grill pan to medium-high heat. Generously oil the grill by drenching a rolled-up paper towel in vegetable oil and rubbing it over the grates.
Remove the chicken from marinade and discard any excess. Grill the chicken, turning once halfway through, for about 4 to 6 minutes per side or until juices run clear.
Transfer the chicken to a plate, cover with foil, and let it rest for a few minutes. Chop into bite-sized pieces and stir into the sauce until coated.
Serve the Chicken Tikka Masala over freshly cooked rice with warmed naan. Garnish with additional chopped cilantro.
