Bring a large pot of salted water to a boil. Add the noodles and cook until al dente, about 8 minutes. Drain, rinse with cold water and place in a large mixing bowl.
In a blender, combine the soy sauce, peanut butter, sesame oil, brown sugar and chili paste. Blend until the sauce is smooth and has a thick but pourable consistency. If it is too thick, add a tablespoon or 2 of hot water to thin. Add the sesame seeds and give it a quick pulse.
Pour the sauce onto the noodles and mix thoroughly to coat. Mix in the scallions, cucumbers and carrots and toss to coat. Refrigerate until ready to serve.
If you can't find mini English cucumbers substitute 1/2 large English cucumber, diced. If you use regular peanut butter reduce the amount of brown sugar to 1 tablespoon. If using regular peanut butter, reduce the amount of brown sugar to 1 tablespoon.
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