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In a small bowl or jar, make the sauce by combining the coconut aminos, broth, lime juice, sesame oil, garlic, ginger, red pepper flakes, and pepper. Add two tablespoons of the sauce in another small bowl along with the arrowroot flour and mix well. Set both of them aside.
Liberally season the sliced steak with salt and pepper. Heat a large skillet over medium heat, add oil, and let it get hot. Add slices of beef, without overcrowding, and cook 30 seconds per side. Remove from pan and repeat with remaining beef (I had to do this in 3 batches).
Leaving the beef juices in the pan, add broccoli. Add 2 tablespoons of the stir-fry sauce (not the one with the arrowroot), mix well, and cover with a lid. Cook for 3-5 minutes until tender. Remove from the pan and set aside (leave behind any juices).
Add remaining sauce as well as the arrowroot sauce to the pan, mixing to combine. Reduce to medium-low and cook until thickened and coats the back of a spoon (nappe consistency), about 2-3 minutes. Add the beef and broccoli back to the pan, leaving behind their juices, and stir to combine and heat through about 1 minute. Be careful not to add the liquid from the beef and broccoli as it will thin the sauce.
Serve with cauliflower or white rice, top with optional toppings, and enjoy!