Cook the soba noodles in boiling water according to package directions, then drain and set aside.
In a small bowl, whisk together the tamari, honey, water, arrowroot powder, and red pepper flakes to create the sauce.
Heat the sesame oil in a large skillet over medium-high heat until shimmering.
Add the thinly sliced flank steak to the skillet and sear until browned, approximately 2-3 minutes, then remove from the pan.
Add the broccoli, bell pepper, minced garlic, and grated ginger to the same skillet, sautéing until the vegetables are tender-crisp.
Return the beef to the skillet and pour in the sauce, stirring constantly until the sauce thickens and coats the ingredients.
Toss in the cooked soba noodles and sliced green onion, mixing well to incorporate all flavors before serving.