Cook the noodles according to the package directions until al dente. Drain and rinse them.
Saute tofu in 1 teaspoon of sesame oil over medium heat, tossing occasionally, until golden brown and cooked through, about 10 minutes.
Meanwhile, make the sauce: In a large measuring cup, whisk together the ketchup, soy sauce, lime juice, sugar, vinegar and 2 teaspoons of the sesame oil.
In a large nonstick skillet, heat the remaining sesame oil over medium heat. Add the onions and carrots and stir-fry for several minutes until they are slightly softened, about 3-4 minutes. Add the cooked noodles, sauce, cooked tofu, and cilantro or basil. Toss to combine until heated through. Serve with Stir-Fried Sesame Broccoli.
To make the Broccoli:
Heat 1 T sesame oil in a large skillet. Lightly brown garlic, about 30 seconds. Add broccoli pieces and 2 T water. Cover and cook over medium-high heat for about five minutes. Add soy sauce and stir-fry for 1 minute more before serving.