Slice the flank steak against the grain into thin strips and place them into the slow cooker.
In a small mixing bowl, whisk together the coconut aminos, beef broth, honey, sesame oil, minced ginger, minced garlic, red pepper flakes, sea salt, and black pepper.
Pour the sauce mixture over the beef strips and stir until every piece is well-coated.
Cover the slow cooker and cook on low for 4 to 5 hours or on high for 2 to 3 hours until the beef is tender.
In a small ramekin, mix the arrowroot powder with one tablespoon of cold water to create a smooth slurry.
Stir the slurry into the slow cooker liquid and cook on high for an additional 15 minutes to thicken the glaze.
Steam the broccoli florets separately in a steamer basket for 3 to 4 minutes until tender-crisp and bright green.
Gently fold the steamed broccoli into the beef mixture and serve immediately over the warm cooked brown rice.