Heat the oils in a large skillet over medium-high heat. Add chicken and cook for about 7 minutes, flip and add in broccoli florets. Cook for five minutes.
Meanwhile, stir together tamari sauce, honey, lime juice, grated ginger, and grated garlic. Add to skillet and stir well.
Whisk together water and cornstarch. Add to skillet. Cook, stirring occasionally, until the sauce has reduced by about half and has thickened to a desired consistency.
Serve with cooked rice; enjoy!
Notes
You'll use about one clove of garlic and ½ inch piece of fresh ginger to get 1 teaspoon each.