In a small bowl, whisk together the coconut aminos, arrowroot powder, grated ginger, and water to create a smooth slurry for the sauce.
Season the thinly sliced flank steak evenly with the sea salt and black pepper.
Heat the toasted sesame oil in a large skillet or wok over medium-high heat until it begins to shimmer.
Add the beef to the hot pan in a single layer and sear until deeply browned and caramelized, about 2 minutes per side, then remove the beef and set it aside on a plate.
Add the broccoli florets and sliced red bell peppers to the same skillet with a splash of water, then cover with a lid for 2 minutes to steam until they are crisp-tender.
Remove the lid, add the minced garlic, and sauté for 30 seconds until the aroma is released.
Return the cooked beef and any accumulated juices to the skillet, then pour the prepared sauce over the mixture.
Toss everything together constantly for 1 minute until the sauce thickens into a glossy glaze that coats the beef and vegetables.
Garnish the stir-fry with sesame seeds and serve immediately while hot.