Soak udon noodles in hot water to loosen them while you proceed with the remaining steps.
In a small bowl or measuring cup, combine, the soy sauce, vegetable broth, rice vinegar, sesame oil, and chili oil.
Heat 1 tablespoon of oil in a large pan over medium high heat. Add the garlic and ginger and cook, stirring constantly for 30 seconds.
Add the carrots, and cook stirring constantly about 1 minute.
Add the mushrooms and green onions and cook 1 minute.
Add the toy choy and stir fry about 2 minutes longer until crisp tender.
Add the udon noodles and cook, stirring to combine with the vegetables, about 2 minutes longer.
Add the soy sauce mixture and toss to combine until the sauce thickens and coats the noodles. Stir fry another minute or two to heat.
Sprinkle with green onions and sesame seeds and serve.