Slice your beef into thin strips. I like to do this with the meat partially frozen. That way you can cut it extra thin without too much effort. Just place the beef in the freezer for about an hour before slicing.
In a bowl, mix together 2 tbs of cornstarch, 2 tbs of water and 3 cloves of garlic. Then add the sliced beef. Toss to fully coat.
Preheat a large fry pan or wok over high heat. Add two tablespoons of oil to the hot pan and then immediately add the beef mixture. Stir-fry the beef until browned. This will take roughly 5-6 minutes. Remove the beef to a bowl and set aside.
Add 1 tbs oil and the frozen mixed vegetables to the hot wok and cook for 6-8 minutes or until softened.
While the vegetables are cooking mix the 1/3 cup soy sauce, 1/2 cup water, 1 1/2 tbs of cornstarch, 2 tbs brown sugar, 1 tsp ginger, and remaining two cloves of garlic in a bowl.
Once the vegetables are softened, add the beef back to the wok and mix.
Add the sauce, bring to a boil and cook until thickened. Roughly 3-5 minutes.
Remove from the heat and serve over warm rice.