Begin by mixing together all of the ingredients for the marinade (garlic, ginger, apple juice, soy sauce, vinegar, honey, and red pepper flakes).
Slice the steak into thin strips.
Add the steak into the marinade and mix a bit with your hands.
Cover the bowl and set the bowl in the fridge to marinate anywhere from 20-60 minutes.
Meanwhile, wash and chop the onion, carrot, and broccoli.
After the meat is done marinating, heat a large skillet over medium high heat and add two teaspoons of olive oil.
Once the oil is heated, take the meat out of the marinade with a pair of tongs and place into the skillet. There should be some marinade remaining in the bowl, don't discard it! We will be using it.
Cook the beef until the juices are reduced down and the meat begins to caramelize, about 4-6 minutes. You should be monitoring and stirring the meat during this time.
Remove the meat from the pan and place into a bowl.
Return the skillet to the burner and add in the remaining two teaspoons of oil, along with the chopped onion.
Saute the onion for about 30 seconds, then add in 1/4 cup of water.
Let the onion continue to cook until softened, about 2-3 minutes.
Add in the grated carrot and cook another 1-2 minutes.
Stir in the remaining 1/2 cup of water, along with the chopped broccoli and cook for 2-3 minutes until the broccoli is bright green.
While the broccoli is cooking, whisk the arrowroot into the remaining marinade.
Pour the marinade mixture into the pan of cooking broccoli and stir until it appears to thicken (about 30-60 seconds).
Remove the pan from the heat and add the meat back in.
Give everything one final stir and serve immediately with brown rice or how you like.