Cook noodles according to package instructions until just tender (or longer, if you prefer a softer texture that absorbs sauce more easily). Drain, rinse well with cool water, and set aside. Cut cucumbers into 1/2- by 1 1/2-in. pieces. Set aside.
Whisk together soy sauce, vinegar, oil, peanut butter, and molasses in a large bowl; set aside.
Lightly brown sausage in a large frying pan over medium-high heat, stirring, 3 to 4 minutes. Drain on paper towels.
Add drained noodles to peanut butter sauce, tossing to coat, then add sausages, cilantro, basil, and about two-thirds of cucumbers. Line 4 wide, shallow bowls with salad greens and add pasta. Top with remaining cucumbers and sprinkle with peanuts.
*Find at well-stocked grocery stores, Asian markets, and amazon.com.