Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add the chopped chicken breasts, season with salt and pepper; and cook until browned and most cooked; about 5 minutes.
Make the Stir-Fry Sauce while the chicken is cooking -- whisk the ingredients together and set aside.
Once the chicken is browned, add the remaining 1 tablespoon olive oil to the skillet along with the broccoli. Continue cooking for another 3 to 4 minutes, or until the broccoli is bright green. Stir in the sauce and cook for another minute, or until the sauce has thickened. Remove from heat and stir in the sesame oil.
Serve over steamed grains, garnished with green onions. Can be refrigerated in an airtight container for up to 3 days.
