Cook the soba noodles in a pot of boiling water for 4-5 minutes until tender, then drain and rinse with cold water to prevent sticking.
Slice the flank steak very thinly against the grain into bite-sized strips.
In a small bowl, whisk together the tamari, minced fresh ginger, and minced garlic to create the stir-fry sauce.
Heat the toasted sesame oil in a large skillet or wok over medium-high heat.
Add the steak strips to the hot skillet and sear until browned on all sides, approximately 2-3 minutes.
Add the broccoli florets and sliced red bell peppers to the skillet, sautéing for 3-4 minutes until the vegetables are bright and tender-crisp.
Add the cooked soba noodles and the prepared sauce to the skillet, tossing everything together until well-coated and heated through.
Garnish the dish with sesame seeds, sliced green onions, and red pepper flakes before serving immediately.