Whisk together sesame oil, cornstarch, 1 tablespoon soy sauce, salt, and baking soda together in a bowl. Add sliced steak to the bowl and marinate for 10 minutes.
Meanwhile, whisk mirin, water, 3 tablespoons soy sauce, dark soy sauce, sweet soy sauce, oyster sauce, and rice vinegar together in a small bowl; set sauce aside.
Bring a large pot of lightly salted water to a boil over high heat.
Heat a wok over medium high heat, cook and stir steak in the hot wok until steak pieces are caramelized and browned, 3 to 4 minutes. Remove steak from wok; set aside to keep warm.
Add broccoli to the wok with a small amount of water. Cover with a lid and steam broccoli until bright green, about 5 minutes.
Add udon noodles to boiling water; return water to a boil and cook until noodles are tender with a bite, 2 to 3 minutes.
Add garlic and ginger to the wok. Return steak to wok.
Drain noodles; stir noodles and prepared sauce into the wok to combine. Sprinkle with green onions, black sesame seeds, and toasted sesame seeds to serve.