In a medium bowl, whisk together the low-sodium soy sauce, water, red wine vinegar, brown sugar, granulated sugar, minced garlic, and ground ginger to create the teriyaki sauce.

In a small bowl, mix the cornstarch with the warm water until smooth. Whisk this mixture into the teriyaki sauce prepared earlier.

Pour the teriyaki sauce into a saucepan over low heat, simmer gently until it thickens, stirring occasionally for about 5-7 minutes.

Heat the vegetable oil in a large skillet over medium heat. Add the diced onion and minced garlic, sautéing until fragrant and translucent, about 2-3 minutes.

Add the ground turkey to the skillet, breaking it apart with a spatula. Cook until fully browned and no pink remains.

Incorporate the broccoli and grated carrots into the turkey mixture. Stir occasionally, cooking for another 3-5 minutes until the vegetables are just tender.

Pour the thickened teriyaki sauce over the turkey and vegetable mixture. Stir well to combine and let it simmer together for an additional 5 minutes.

To serve, divide the cooked rice into bowls, top with the turkey and vegetable mixture and garnish with diced green onions.