Wash and prep the vegetables: wash and dry the snap peas, cut the bell peppers and onion into thin strips, and chop the scallions and baby bok choy (separating out the leafy greens from the stems).
Combine soy sauce and brown sugar in a small bowl and mix well until sugar is dissolved, then add rice vinegar, sesame oil, minced garlic, and chili garlic sauce (to taste). Stir well to combine and set aside.
Cook the udon noodles according to the package directions.
While the noodles are cooking, heat 2 tbsp vegetable oil in a wok or large skillet over medium heat. Add garlic and snap peas, stirring occasionally until snap peas start to soften, about 6 to 8 minutes.
Add the bell pepper, onion, and scallion and bok choy stalks to the wok with an additional 1 tbsp of vegetable oil. Cook until vegetables soften, about 3 to 5 minutes.
Add the scallion and bok choy leaves to the wok. Stir frequently and cook for another 1 to 2 minutes.
Lower heat and add cooked udon noodles and sauce to the wok. Stir well to combine and serve hot.