In a bowl, combine the coconut aminos and arrowroot starch. Whisk until dissolved and no longer clumpy. Add the steak and toss to coat. Cover and set aside to let marinate for 15 minutes or up to 1 hour.
Preheat a large cast-iron or carbon-steel pan over medium-high heat for 5 minutes. Raise the heat to high, add the avocado oil and heat until shimmering. Reserving the marinade, drain off as much of it as possible from the beef. Carefully add the beef to the hot oil (it will splatter) and cook, undisturbed, until browned, about 2 minutes. Flip the beef and continue to cook until browned on the opposite side, about 1 minute. Transfer the beef to a bowl and set aside.
Lower the heat to medium high and add the carrot, bell pepper, chili pepper, and onion. Stir-fry the vegetables until they have softened slightly, 2 minutes. Add the garlic and cook an additional 60 seconds. Add the reserved marinade and sesame oil and cook, stirring regularly, for 2 minutes. Return the beef to the pan and toss to coat.
Serve with cauliflower rice and enjoy immediately.