In a large mixing bowl, combine the Greek yogurt, lemon juice, ground cumin, paprika, cinnamon, cayenne pepper, ground ginger, salt, and black pepper. Add the chicken pieces and toss until well coated. Cover and refrigerate for at least 1 hour, or overnight for best results.

Preheat your grill to medium-high heat. Thread the marinated chicken onto skewers and grill for 6-8 minutes per side, or until cooked through and slightly charred. Remove from the grill and set aside.

In a large skillet, heat the olive oil over medium heat. Add the chopped onion and cook, stirring occasionally, until softened and translucent, about 5 minutes. Add the minced garlic and grated ginger, and cook for another 1-2 minutes, until fragrant.

Stir in the ground coriander, ground cumin, paprika, turmeric, cinnamon, and cayenne pepper. Cook for 1 minute, until spices are toasted and fragrant.

Add the crushed tomatoes to the skillet and bring to a simmer. Cook for 5 minutes, stirring occasionally.

Stir in the heavy cream and cooked chicken pieces. Simmer for an additional 5 minutes, until the sauce is thickened and the chicken is heated through. Season with salt and pepper to taste.

Serve the chicken tikka masala over cooked rice, garnished with chopped fresh cilantro.