Combine the first 10 ingredients (through garlic) in a small saucepan; stir with a whisk until blended. Bring to a boil; cook, stirring constantly, about 1 minute. Set aside.
Cook the noodles in boiling water for 8 minutes and drain well. Combine the noodles, peanut sauce, bok choy, snow peas, and carrot in a large bowl; toss well to coat.
Notes
To prepare this recipe as GLUTEN FREE, sub in GF pasta for the Udon noodles- and make sure the following ingredients that you have in your pantry are designated as GF: soy sauce and chili garlic sauce.
When cooking for kids, leave out what you know they'll be frowning upon and substitute their favorite veggies in there instead.
Chile paste with garlic and udon noodles can be found with other ethnic foods in your local market or Asian market.
The chili garlic sauce can be omitted if you prefer a not-so-spicy sauce.