Prepare rice according to package instructions. Set aside.
In a small saucepan, add the soy sauce, ¼ cup water, red wine vinegar, sugars, garlic, and ginger over medium heat. Whisk while heating until sugar is dissolved.
In a small bowl, whisk together 2 tablespoons warm water and cornstarch until cornstarch is completely dissolved. Whisk cornstarch mixture to the soy sauce mixture with the stove on medium-high heat. Simmer until the mixture is thick. Remove the saucepan from the heat while you prepare the remaining ingredients.
Cook ground beef, onions, and garlic into a large skillet and cook until the beef is about half cooked. Add chopped carrots and broccoli. Cook until the beef is no longer pink and the carrots and broccoli are tender.
Pour the teriyaki sauce over the beef and vegetables and stir. Simmer for about five minutes to combine the flavors.
Spoon beef and vegetables over rice and serve.