Set oven to broil. Sprinkle chicken breasts on both sides with coriander and cumin. Coat the chicken breasts completely with the plain yogurt. Set the chicken on a metal cooling rack over a foil-lined baking sheet and place it about 10-12 inches below a broiler for 5-7 minutes per side. Watch carefully so as not to burn chicken. It should have slightly blackened edges. Remove from oven.
Dice the onion. In a large skillet heat olive oil over medium-high heat. Toss in the onions and sauté until they are slightly browned. As the onions cook, mince your garlic.
Cut off the outer skin and mince or grate the fresh ginger. Add the garlic and ginger to the onions.
Add about the Garam Masala spice. Add the diced tomatoes. Continue cooking and stirring, scraping the bottom of the pan to deglaze it. Add 1 tablespoon sugar. Let this mixture simmer on medium for about 5 minutes. Add salt to taste.
After the Tikka Masala sauce has had a chance to simmer for a little bit, add in the half and half. Now, chop up your chicken breasts into chunks (you can also shred them if you prefer) and stir them into the Tikka Masala sauce.
Serve the rice with the Chicken Tikka Masala over top.