Cook pasta according to package instructions. Drain, return to pot, and coat with sesame oil.
While pasta is cooking, heat canola oil in large skillet over medium-high heat. Add broccoli, onion, and red pepper and cook, stirring regularly, for about 3 minutes. Add ginger, garlic, edamame, and carrot. Stir for an additional 1 minute while mixture continues to cook.
In small bowl, whisk together broth, soy sauce, brown sugar, and oyster sauce. Add soy sauce mixture and pasta to skillet and stir for an additional 1-2 minutes, or until everything is heated through.