SPICE BLEND and MARINADE: In a small bowl: combine minced garlic, minced ginger, turmeric, garam masala, cumin, coriander, and salt; stir to combine. In another bowl, whisk to combine the yogurt, half of the spice mixture and lemon juice. Halve chicken breasts and pound pieces to even thickness with a meat mallet (or the bottom of a frying pan). Add chicken to the yogurt mixture and stir to coat. Cover tightly (or transfer to a sealable bag) and refrigerate for at least 6 hours and preferably 24 hours. Cover and chill the remaining spice mixture.
SAUCE: Heat vegetable oil in a large, heavy pan over medium heat. Add the finely chopped onion and cook until it begins to soften, about 2-3 minutes. Add in the tomato paste, ground cardamom, and red pepper flakes. Cook, stirring often, until the tomato paste has darkened and onion is soft, about 5 minutes. Add the reserved half of spice mixture and cook, stirring often, until the bottom of pot begins to brown and everything is very fragrant, about 4 minutes (reduce heat if needed; nothing should be smoking/burning).
SAUCE CONT: Add crushed tomatoes, increase the heat, bring the mixture to a boil and then reduce the heat. Simmer, stirring often and scraping up browned bits from the bottom of the pot, until sauce thickens-- about 8 minutes. Stir in the heavy cream and cilantro. Simmer, over lowest heat, stirring occasionally until the sauce thickens, about 30 to 40 minutes. Optional: transfer the sauce to a blender and process until smooth. Alternatively, use a stick blender to puree until smooth. Taste the sauce for any additional seasoning/salt. Depending on the tomatoes you used, you may need 1-2 teaspoons sugar to balance acidity.
COOK CHICKEN: (See Note 1) Preheat a grill or grill pan to medium-high heat (about 400 degrees F.) Generously oil the grill (I drench a rolled-up paper towel in vegetable oil and, holding it with tongs, rub it over the grill grates. Don't skip this step.) Remove chicken from the marinade and discard any remaining marinade. Grill the chicken, turning once halfway through grilling, about 4-6 minutes per side (until the thickest part of the chicken registers 165 degrees F and juices run clear). Transfer the chicken to a plate and cover with foil. Allow the chicken to rest for a few minutes so the juices can re-distribute. Chop into bite-sized pieces. Stir into the sauce until coated, remove and serve over freshly cooked rice (See Note 2) with warmed naan. Add additional chopped cilantro to garnish as desired.