Stir together the ingredients for the orange sauce in a small bowl or measuring cup and set aside until ready to use.
Crack an egg into a large mixing bowl and whisk it well until well-beaten.
Slice the steak into thin strips against the grain.
Add the beef strips to the mixing bowl with the whisked egg and toss until all of the strips are coated with egg.
Add the tapioca flour and black pepper to the mixing bowl and toss until the strips of steak are coated with the flour mixture. Note: this will cause the beef to stick together. This is entirely normal, and the strips will come apart easily once they are cooking in the skillet.
Heat two tablespoons of avocado oil (or cooking oil of choice) to a large non-stick skillet (I use a 12-inch skillet) over high heat. Allow the skillet to warm up for a couple of minutes before adding the steak to the hot oil. Arrange the steak into a single layer (remember, it will be stuck together, which is normal, so it will take a little maneuvering to get it into one layer). If need be, complete this step in two small batches if your skillet isn’t large enough to cook the strips in one layer.
Allow the steak to cook untouched for 2 to 3 minutes, or until it is nice and golden-brown. Flip the steak and continue cooking for another 2 to 3 minutes, or until the other side is golden-brown as well. The steak does not need to be cooked through just yet.
Pour the sauce into the skillet and bring everything to a full boil. Cook, stirring occasionally, until the sauce is thick and the steak has reached your desired level of crisp, about 5 to 8 minutes.
Serve Orange Beef over your choice of steamed brown rice, white rice, cauliflower rice, or with sauteed vegetables.