Easy Teriyaki Noodles

Name: Easy Teriyaki Noodles
Ingredients: 1 tablespoon peanut oil ((or high-heat oil of choice)); 2 scallions, (white and green parts separated and chopped); 2 garlic cloves, (minced); 1 tablespoon freshly grated ginger; 1/3 cup soy sauce; 1/4 cup water; 3 tablespoons organic brown sugar; 2 tablespoons rice vinegar; 2 tablespoons mirin or dry sherry ((optional)); 1/2 teaspoon toasted sesame oil; 6 ounces dried udon noodles; 2 cups fresh broccoli florets; 1 cup julienne cut carrots; 1 cup fresh baby corn, (cut into 1-inch pieces); 2 tablespoons chilled water; 1 tablespoon cornstarch; 1 cup frozen shelled edamame, (thawed); Toasted sesame seeds, (for serving)