Bring a large pot of water to a boil. Add noodles and cook until barely tender, about 5 minutes; they should retain a hint of chewiness. Drain, rinse with cold water, drain again and toss with a splash of sesame oil.
In a medium bowl, whisk together the remaining 2 tablespoons sesame oil, the soy sauce, rice vinegar, sesame paste, peanut butter, sugar, ginger, garlic and chili-garlic paste.
Pour the sauce over the noodles and toss. Transfer to a serving bowl, and garnish with cucumber and peanuts.