Bring a pot of water to a boil and cook the udon noodles according to package directions, then drain and set aside.
In a small bowl, whisk together the tamari, honey, minced ginger, minced garlic, red pepper flakes, and water to create the stir-fry sauce.
Slice the flank steak against the grain into thin, bite-sized strips.
Heat the avocado oil in a large skillet or wok over high heat until shimmering.
Add the steak strips in a single layer and sear for 2 minutes until browned, then remove the beef from the pan and set aside.
Add the broccoli florets and a splash of water to the same pan, covering with a lid for 2 minutes to steam until bright green and tender-crisp.
Return the beef to the pan along with the cooked udon noodles and the prepared sauce.
Toss everything together for 1-2 minutes until the sauce has thickened and coated every ingredient.
Remove from heat and drizzle with toasted sesame oil before serving.