Bring a large pot of water to a boil. Add the salt, and cook the noodles according to package instructions. Drain the egg noodles two minutes before they are supposed to be done and set aside.
Combine the broth, soy sauce, cornstarch, sugar, sesame oil, and pepper in a small bowl.
Heat 12 teaspoons of oil in a big skillet or wok over high heat, then add the shrimp and cook for 2 minutes, or until almost (but not quite!) done. Place them on a plate and set them aside.
In the same skillet, add the remaining 12 tablespoons of oil, the garlic, broccoli, carrots, and red pepper, and cook for 3 to 4 minutes, or until everything starts to soften.
Return the shrimp, the drained pasta, and the sauce to the pan. Toss over high heat for about two minutes (tongs are fantastic for this) until the noodles absorb some of the sauce, everything is well combined, and the remaining sauce is somewhat thickened.
Serve immediately. You can substitute the shrimp with any protein of your choice such as tofu, chicken, or beef!