Combine the coconut aminos/tamari, broth, vinegar, olive oil, and date in a small bowl and set aside.
Heat 1 tablespoons of coconut oil in a large skillet over high heat.
Add the chicken and lightly brown, then set aside.
Add a second tablespoon of coconut oil and toss the broccoli in. Stir fry lightly, then remove and set aside.
Add 1 tablespoon coconut oil, garlic, and ginger to pan and cook for just a few seconds, add the mushrooms and then add the liquid mixture and simmer for about 30-60 seconds or until thickened.
Return broccoli and chicken to the pan and cook, turning once, until glazed with the sauce, about 1 minute.