Slice the flank steak against the grain into thin, bite-sized strips.
Whisk together the tamari, sesame oil, honey, minced ginger, and minced garlic in a medium bowl.
Add the beef to the marinade, tossing to coat, and let it marinate for 15 minutes.
Heat a large cast-iron skillet over medium-high heat until very hot.
Add the beef in a single layer and sear until deeply browned and caramelized, about 2 minutes per side.
Remove the beef and add the sliced carrots and chopped bok choy to the skillet, sautéing for 3 minutes until tender-crisp.
Divide the cooked brown rice into bowls and top with the beef and vegetables.
Garnish with sesame seeds and sliced green onions before serving.