Bring a large pot of water to a boil. Add the salt to the water, return the water to a boil and cook the pasta according to package directions, stopping two minutes or so before it is fully cooked. Drain the pasta.
Meanwhile, in a small bowl or container, combine the broth, soy sauce, cornstarch, sugar, sesame oil, and pepper.
In a large skillet or wok over high heat, heat 1 ½ teaspoons of the oil, then add the shrimp and sauté until the shrimp are almost (but not quite!) cooked, about 2 minutes. Transfer them to a plate and set aside. Add the remaining 1 ½ teaspoons of oil to the skillet, add the garlic, broccoli, carrots, and red pepper and sauté for 3 to 4 minutes until everything starts to soften.
Return the shrimp to the pan along with the drained pasta and the sauce. Toss (tongs are great for this) over the high heat until the noodles absorb some of the sauce , everything is well mixed, and the rest of the sauce is slightly thickened, another 2 minutes or so. Serve hot.