In a large bowl, combine the chicken pieces, plain yogurt, and half of the tikka masala paste; cover and refrigerate to marinate for at least 10 minutes or up to 4 hours.
Heat 2 tablespoons of the olive oil in a non-stick skillet over medium heat. Add the curry leaves and cook until fragrant, about 30 seconds.
Add the chopped onion, de-seeded chopped chili, and minced garlic to the skillet and cook, stirring, until the onion is translucent, about 2 minutes.
Stir in the remaining tikka masala paste, chicken broth, canned diced tomatoes, and tomato paste. Reduce heat to low and simmer, stirring occasionally, until the sauce thickens, about 15 minutes.
Meanwhile, heat the remaining oil in a separate pan over medium-high heat. Add the marinated chicken in a single layer and cook until golden and slightly crisp on the outside, turning as needed.
Transfer the cooked chicken to the simmering sauce, reduce heat to low, and simmer together for 10 minutes so the flavors combine and the chicken finishes cooking.
Stir the heavy cream into the sauce until combined, warm through, and serve immediately.
