Cook the spaghetti or linguine according to package instructions until al dente. Drain and rinse under cold water to cool. Set aside.
In a medium bowl, whisk together the peanut butter, soy sauce, rice vinegar, sesame oil, honey (or maple syrup), grated ginger, minced garlic, and water until smooth. If the sauce is too thick, add more water, one tablespoon at a time, until desired consistency is reached.
In a large bowl, combine the cooled noodles, cucumber, carrots, and green onions. Pour the peanut sauce over the noodle mixture and toss until everything is well coated.
Serve immediately or chill in the refrigerator for 30 minutes to enhance the flavors. If serving later, give the noodles a quick toss before serving.
Garnish with sesame seeds and fresh cilantro if desired.