Cook the soba noodles in boiling water according to package directions, drain, and set aside.
Slice the flank steak into thin strips against the grain and season evenly with sea salt and black pepper.
Heat the sesame oil in a large wok or cast-iron skillet over medium-high heat until it begins to shimmer.
Add the beef strips to the hot pan and sear for 2-3 minutes until browned, then remove the beef and set it aside on a plate.
In the same pan, add the broccoli florets, sliced bell peppers, minced ginger, and minced garlic, sautéing for 3-4 minutes until the vegetables are tender-crisp.
Return the beef and cooked soba noodles to the wok, pour in the tamari, and toss everything together for 1 minute until well-combined and heated through.
Transfer to a bowl and garnish with sesame seeds before serving.