In a small bowl, combine all sauce ingredients in no particular order. Use a whisk to mix well.
Cook linguine using directions on the package. Add carrots and snow peas while still cooking pasta.
Drain in a colander over a pasta bowl while keeping 1/4 cup liquid.
Place pasta mixture, bell pepper, and onions in a large bowl.
Combine sauce and 1/4 cooking liquid.
Pour over pasta mixture; toss well until well combined. Serve warm.