Combine the ground cumin, coriander, cardamom, cinnamon, nutmeg, clove, turmeric, smoked hot paprika and ground ginger to make the spice mix.
In a bowl whisk together the yogurt, 5 teaspoons of the tikka masala spice blend, 1 teaspoon salt, 4 minced garlic cloves, and 2 teaspoons lemon juice until smooth.
Toss the cubed chicken with the yogurt marinade, cover, and refrigerate 8 to 10 hours.
When ready, remove the chicken from the marinade and pat lightly with paper towels to remove excess.
Thread the chicken onto skewers and grill over medium-high heat until cooked through and slightly charred on the edges, about 6–8 minutes per side depending on size; remove from skewers and set aside.
In a Dutch oven, melt the butter over medium heat.
Add the minced onion and cook, stirring occasionally, until soft and translucent, about 5 to 7 minutes.
Add the remaining tikka masala spice blend and 8 minced garlic cloves and cook, stirring, for about 1 minute until fragrant, then stir in the tomato paste and cook another minute.
Add the crushed tomatoes, heavy cream, and 1/4 teaspoon salt; stir to combine and bring to a gentle simmer.
Stir the grilled chicken into the sauce and heat through, about 3 to 5 minutes. Taste and adjust salt if needed.
Serve the chicken tikka masala with rice or naan and sprinkle with finely chopped cilantro, if using.