To make the sauce, combine the ginger, garlic, maple syrup, peanut butter, rice vinegar, soy sauce, olive oil, and 1 tablespoon of sesame oil in a food processor or blender. Process until smooth and set aside.
Cook the noodles in a large pot of water according to the package directions. Before draining the noodles, measure out a half cup of the cooking water and set it aside. Drain the noodles and place them in a large bowl. Add the remaining tablespoon of sesame oil to the noodles and stir.
Mix the peanut butter dressing with the half cup of cooking water. Pour this sauce over the hot noodles and stir. Leave the noodles at room temperature for up to 60 minutes, stirring occasionally to help the noodles soak up the sauce.
When you’re ready to serve the noodles, stir in the scallions, carrots, and sesame seeds. This dish can be served warm or at room temperature.