Make Sauce: In a small mixing bowl, add ½ cup coconut aminos, ¼ cup chicken broth, 3 tablespoons rice vinegar, 1 tablespoon arrowroot powder, 1 tablespoon orange juice, 1 tablespoon fresh ginger, 3 cloves garlic, 1 teaspoon sesame oil, and a pinch kosher salt. Whisk to combine and set aside.
Heat Pan: Take a large cast iron skillet and bring to medium heat. Add 1 tablespoon of ghee. Let it melt and coat the pan.
Prep Stations: Place 2-3 tablespoons arrowroot powder in a medium-sized bowl. Place the sliced steak and arrowroot on the counter next to your cast iron skillet.
Sear Steak: Working in batches, lightly place pieces of beef in the arrowroot and lightly coat them. Shake off any excess and add to the pan. Continue, spacing out the beef strips so they aren't touching, until you have filled up the cast iron skillet. Lightly season with kosher salt and ground black pepper. Cook the strips approximately 1 minute per side, remove, and place on a clean plate. Continue until all the beef is seared on both sides (this should take about 3-4 batches) adding a tablespoon of ghee (or more) in between each batch to keep the bottom of the skillet from drying out.
Veggies: Once the steak is all cooked and set aside, add approximately ¼ cup coconut aminos to pan to deglaze (scraping up all the bits from the bottom). Add 4 cups broccoli florets and 1 pint mushrooms and stir and cook for about 5 minutes.
Combine: Add sauce (whisk the sauce again before adding as the arrowroot may sink to the bottom) and bring to a light simmer. Stir until it starts to thicken, about 2 minutes. Add steak (along with any juices that have settled on the plate) and stir to fully mix.
Serve: Remove from heat and enjoy immediately. If you want to keep it Paleo/Whole30, you can eat it plain or with some easy cauliflower rice. If you aren't concerned with Paleo/Whole30, then I would suggest serving it with some Instant Pot brown rice!
Notes
Searing the beef: When cooking the beef in the cast iron skillet, feel free to really just sear the strips on both sides. If you really don't like more of a medium/medium-rare beef then cook it a bit longer.