Heat a large skillet over medium-high heat and add the ground beef, sea salt, and black pepper, breaking it up with a spatula until browned and cooked through.
Remove the browned beef from the pan and set it aside, leaving any rendered fat in the skillet.
Add the broccoli florets to the skillet with a splash of water, then cover with a lid for 2 minutes to steam until they are bright green and tender-crisp.
In a small bowl, whisk together the coconut aminos, toasted sesame oil, grated fresh ginger, minced garlic, arrowroot powder, and water to create a smooth sauce slurry.
Return the cooked beef to the skillet with the broccoli and pour the sauce over the mixture.
Stir-fry everything together for 1 to 2 minutes until the sauce thickens into a glossy glaze that coats the beef and broccoli evenly.
Serve immediately while hot and the broccoli maintains its vibrant color.