Boil a pot of water and cook the soba noodles according to the package instructions until al dente, then drain and set aside.
Slice the flank steak into very 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 shimmering.
Add the beef strips to the pan in a single layer and sear for 2 minutes until browned and caramelized, then remove the beef and set it aside on a plate.
In the same pan, add the broccoli florets and sliced red bell pepper, stir-frying for 3-4 minutes until the vegetables are bright and tender-crisp.
Add the minced garlic, grated ginger, and red pepper flakes to the vegetables, stirring constantly for 30 seconds until highly fragrant.
Return the cooked beef and any juices from the plate back into the pan along with the cooked soba noodles.
Pour the tamari over the mixture and toss everything together for 1 minute to ensure the noodles and beef are thoroughly coated and heated through.
Transfer to a bowl and garnish with sesame seeds before serving hot.