In a mixing bowl, whisk together soy sauce, water, vinegar, sugars, garlic, ginger, cornstarch, and warm water to make the teriyaki sauce.
Heat vegetable oil in a non-stick skillet over medium heat. Sauté onions and garlic until fragrant, then add broccoli and carrots until tender.
Add ground turkey to the skillet and cook until browned.
Pour in the teriyaki sauce and stir well. Simmer for about 5 minutes until thickened.
Serve over cooked rice and garnish with green onions.
