In a large skillet (that has a tight fitting lid for later), heat the olive oil over medium high heat.

Season chicken with salt and pepper. Add the chicken to the skillet and cook for 1-2 minutes just to brown the outside of the chicken. The chicken will continue to cook in the broth later. Add the garlic and cook for 30 seconds.

Add the chicken broth, rice, carrots, teriyaki sauce (add the ingredients for homemade if using), and soy sauce.

Bring mixture to a boil. Reduce heat to medium and cover with a lid. Cook covered for 15 minutes, reducing the heat to a simmer after about 10 minutes. Stir every once in a while to make sure it's not sticking to the bottom. You want it to be simmering but if your heat is too high you will run out of liquid, so make sure it's low.

Add the broccoli on top, cover with lid and cook for an additional 5 minutes on medium-low or until broccoli is tender. If you like your broccoli more cooked, add it earlier.

Remove from heat and sprinkle with green onions. Drizzle with sesame oil if using and drizzled with more teriyaki sauce if desired. Add salt and pepper to taste.