In a small bowl, whisk together soy sauce, brown sugar, ginger, garlic, sesame oil, red pepper flake and ground black pepper; set aside.
In a large pot of boiling water, cook udon noodles according to package instructions; drain well.
Heat olive oil in a large cast iron skillet over medium high heat. Add beef and cook, flipping once, until browned, about 3-4 minutes; set aside.
Stir in mushrooms, broccoli and carrots to the skillet. Cook, stirring frequently, until tender, about 3-4 minutes. Stir in udon noodles, beef and soy sauce mixture until well combined, about 2-3 minutes.
Serve immediately
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