In a mixing bowl, combine the diced chicken breasts with tikka masala paste and Greek yogurt. Let the chicken marinate for at least 10 minutes while you prepare the other ingredients. This gives the chicken a bold flavor and keeps it tender.

Heat olive oil in a large pot over medium heat. Add chopped onions and sauté until they are soft and translucent, about 5 minutes. Then, add minced garlic and grated ginger. Cook for another minute until fragrant.

To the onion mixture, stir in ground cumin, coriander, turmeric, and paprika. Let the spices bloom for 1-2 minutes, stirring frequently to prevent burning. This helps release their essential oils and flavors, enhancing the soup's depth.

Add the marinated chicken to the pot and cook for about 5-7 minutes, stirring occasionally, until the chicken is browned on the outside. Don’t worry if it's not fully cooked—it will finish cooking in the broth.

Stir in the tomato paste, diced tomatoes, chicken broth, and coconut milk. Bring the soup to a boil, then reduce the heat and let it simmer for 15 minutes. This allows the flavors to meld beautifully.

Once the chicken is fully cooked, use an immersion blender to blend the soup to your desired consistency. You can leave it chunky or make it smooth and creamy. If you prefer a smooth soup, transfer it to a blender and blend in batches.

Taste the soup and adjust the seasoning with salt, pepper, and red chili flakes for extra heat if you like. Ladle it into bowls, garnish with fresh cilantro, and serve with lemon wedges on the side.