Whisk together cornstarch, oyster sauce, miso, sesame oil, and 2 tablespoons mentsuyu in a medium bowl. Add steak, and toss until steak is evenly coated. Set aside.
Toss together cabbage, ginger, and salt in a large bowl. Let stand until cabbage begins to release water, about 5 minutes.
Heat canola oil in a large nonstick skillet over medium-high. Add steak; cook, stirring occasionally, until steak is no longer pink, 3 to 4 minutes. Add onion, cabbage mixture, and remaining ½ cup mentsuyu. Cover and cook, stirring occasionally, until cabbage is tender, 8 to 10 minutes.
Uncover skillet; cook, stirring often, until sauce thickens enough to coat cabbage and beef, 1 to 2 minutes.
Remove skillet from heat. Garnish with shichimi togarashi; serve with noodles or rice and additional mentsuyu for dipping.
