Make the curry paste: In a blender or food processor, combine the quartered onion, halved shallot, garlic cloves, peeled ginger pieces, garam masala, turmeric, kosher salt, crushed red pepper flakes, and lemon zest. Blend until very smooth, about 1 minute.
Marinate the chicken: Put 2 tablespoons of the curry paste, the cubed chicken, and the Greek yogurt into a gallon-size zip-top bag. Seal and massage to coat the chicken evenly. Marinate at room temperature for 30 minutes or refrigerate up to overnight.
Cook the sauce and chicken: Heat a large high-sided skillet over medium heat. Add 1/4 to 1/2 cup of the curry paste (use to taste) and cook, stirring, until fragrant, about 1 minute.
Add the marinated chicken, coconut milk, and tomato paste to the skillet. Stir to combine, then cover and cook until the chicken is cooked through, 15 to 20 minutes.
Finish the sauce: Remove the lid and simmer until the sauce thickens slightly, about 5 minutes more. Stir in the chopped cilantro.
Serve: Spoon the chicken tikka masala over the cooked rice and enjoy.