In a large pot of boiling salted water, cook the pasta according to package directions. Drain the pasta well, rinse it under cold water, and transfer to a large bowl. Add the carrots and scallions.
In a small bowl, combine the garlic, soy sauce, vinegar, sesame oil, peanut or vegetable oil, ginger, and red pepper flakes. Pour over the noodles and toss to combine. Serve garnished with white sesame seeds.