In a small bowl mix the Teriyaki sauce ingredients. If you are just making the sauce for future consumption follow this step otherwise follow the next paragraphs.
In a small sauce pan, over medium to low heat, heat the sauce until thicken stirring occasionally. About 5 minutes.
Let the sauce cool and store it in a glass airtight container in the refrigerator.
In a large skillet, over medium to high heat, add the olive oil.
Add the chicken and carrots and cook stirring occasionally until almost tender, about 6-8 minutes.
Add the garlic and cook further for another minute.
While the chicken is cooking, place the broccoli on a safe microwave dish and microwave for 6-7 minutes. Depending on how strong your microwave is you may need less time. My microwave is not too powerful so I use 7 minutes but 3-4 minutes may be enough in yours.
Add the Teriyaki sauce from the bowl to the chicken and carrots and stir for about 1-2 minutes or until it thickens.
Turn heat off and add the broccoli and pepper flakes if using. Stir to combine.
Serve over brown rice or rice noddles.