In a large bowl, combine all Chicken Tikka ingredients (yogurt, lemon juice, ginger, garlic, garam masala, smoked paprika, turmeric, cumin, chili powder, and salt). Add chicken pieces and toss to coat evenly. Cover and refrigerate for at least 1 hour, preferably 4–6 hours or overnight for deeper flavor.
Preheat grill to high heat or set oven broiler rack about 6 inches from heat. Thread marinated chicken onto metal or soaked bamboo skewers. Drizzle with a little oil. Grill or broil, turning once, until charred and cooked through, about 8–10 minutes total (internal temp 165°F). Remove from skewers and set aside.
In a large heavy skillet or Dutch oven, heat 2 tbsp ghee over medium heat. Add diced onion and cook, stirring often, until deeply golden brown, about 10–12 minutes. Add ginger and garlic, cook 1 minute until fragrant. Stir in ground coriander, garam masala, cumin, and smoked paprika; toast for 30 seconds.
Add tomato paste and stir for 1 minute. Pour in the tomato puree, water, and sugar (if using). Bring to a simmer, reduce heat to low, and cook gently for 10–12 minutes, stirring occasionally, until sauce thickens slightly. Stir in heavy cream and simmer for another 3–4 minutes. Taste and adjust salt and spices.
Add the cooked chicken tikka pieces to the sauce. Stir well to coat and let them heat through for 2–3 minutes. If sauce is too thick, add a splash of water or cream. Turn off heat.
Spoon the chicken tikka masala into a serving bowl, drizzle with a little extra cream, and scatter fresh cilantro. Serve immediately with steamed basmati rice or warm naan bread.