Cook udon noodles according to package instructions, then rinse in cold water and set aside.
In a large skillet or wok, heat oil over medium-high heat.
Add onions and sauté until translucent.
Add bell pepper and shiitake mushrooms and sauté until tender.
Add bok choy, garlic, and ginger, and stir-fry for 1-2 minutes.
Add cooked udon noodles to the skillet and stir to combine.
In a small bowl, whisk together soy sauce, vegan oyster sauce, sugar, salt, and pepper.
Pour sauce over udon and vegetables and stir-fry for an additional 2-3 minutes.
Serve hot, garnished with chopped green onions.