Prepare the brown rice according to the package instructions until fluffy.
Slice the flank steak against the grain into thin, bite-sized strips and season with sea salt and black pepper.
In a small jar, whisk together the coconut aminos, minced ginger, minced garlic, arrowroot powder, and water until smooth.
Heat the toasted sesame oil in a large skillet or wok over medium-high heat until shimmering.
Add the steak to the skillet in a single layer and sear until deeply browned, about 2-3 minutes, then transfer to a plate.
Toss the broccoli florets into the same skillet with a tablespoon of water, then cover with a lid to steam for 3 minutes until vibrant green.
Return the beef to the skillet and pour the prepared sauce over the mixture, tossing constantly until the glaze thickens and coats everything.
Serve the beef and broccoli immediately over the warm brown rice.