01 - In a large bowl, combine Greek yogurt, lemon juice, ginger paste, garlic paste, ground cumin, coriander, chili powder, turmeric, and salt. Add chicken pieces, toss to coat thoroughly. Cover and refrigerate for at least 1 hour, preferably overnight for maximum flavor penetration.
02 - Bring 4 cups water to a rolling boil. Add salt, bay leaves, cardamom pods, cloves, and cinnamon stick. Stir in soaked basmati rice. Cook until grains are 70% done, approximately 7-8 minutes. Drain thoroughly in a fine mesh strainer and set aside, discarding whole spices if preferred.
03 - Heat butter and vegetable oil in a large skillet over medium heat. Add finely chopped onion and sauté until golden brown, about 5-7 minutes. Stir in ginger and garlic paste, cook for 1 minute until fragrant.
04 - Add marinated chicken to the skillet. Cook until lightly browned on all sides, about 6-8 minutes. The chicken should develop a slight crust while releasing excess moisture.
05 - Sprinkle garam masala, ground cumin, paprika, and chili powder over the chicken. Stir continuously for 1 minute to bloom the spices. Pour in crushed tomatoes and simmer for 10 minutes until reduced slightly. Add heavy cream and sugar, season with salt to taste. Simmer until sauce thickens and chicken is fully cooked through, about 10-15 minutes. Fold in chopped cilantro.
06 - In a large ovenproof Dutch oven or heavy pot, spread half the butter chicken sauce evenly across the bottom. Top with half the par-cooked rice. Drizzle with half the saffron milk, melted butter, fried onions, cilantro, and mint. Repeat with remaining sauce, rice, saffron milk, butter, fried onions, cilantro, and mint to create alternating layers.
07 - Cover the pot tightly with aluminum foil or a secure lid. Bake at 350°F for 25 minutes, or cook on the stovetop over very low heat for the same duration. Remove from heat and let rest for 10 minutes. Gently fluff with a fork, mixing layers just before serving.