Combine the 2 tablespoons of soy sauce, 1 teaspoon sesame oil, 2 thinly sliced green onions, cornstarch, and sliced pork; toss to coat and let stand for 15 minutes.
Meanwhile, combine the sauce ingredients; set aside.
Cook the noodles following package directions; drain in a colander under cold water. Toss with the 2 teaspoons of sesame oil and set aside.
In a wok or large skillet, heat 2 tablespoons of oil; add the green onions and ginger paste and cook, stirring, for about 1 minute. Add the pork with marinade and cook, stirring constantly, until pork is browned and cooked through. Remove to a plate and set aside.
Add 2 more tablespoons of oil to the skillet and cook the broccoli until it just begins to be tender. Remove and set aside.
Add 1 or 2 tablespoons of oil to the wok or skillet and add the noodles. Cook, stirring frequently, until hot. Remove to a serving dish.
Add the Pork, broccoli, and sauce mixture to the skillet and cook, stirring, for 1 to 2 minutes, until thickened and hot.
Pour the pork mixture over the hot noodles and sprinkle with sesame seeds and green onions, if desired.