Combine all sauce ingredients in a small bowl and set aside.
Fill a small saucepan with water and bring to a boil. Cook udon according to directions. Drain and set aside. (Leave about a tbsp of water at the bottom of the pan so the noodles don't stick.)
Fry each egg sunny-side up and set aside.
Warm oil in a large pan over medium-high heat. Once warm, add mushrooms and spread into one layer. Let cook 3-5 minutes without stirring. Add broccoli and stir. Cook 2 minutes then pour in 2 tbsp water and cover. Cook 2 more minutes until broccoli is tender-crisp. Add the Libby's Whole Kernel Sweet Corn, Libby's Sliced Carrots, noodles, and sauce. Gently stir to coat. Once ingredients are warmed through, remove from heat. Serve immediately.