Bring a large pot of water to a boil.
Add the noodles to the boiling water.
Cook for approximately 5 minutes, or until the noodles are just tender and still slightly al dente.
Drain the noodles in a colander.
Rinse the noodles thoroughly under cold water to stop the cooking process and cool them completely.
Allow the noodles to drain well.
Return the drained noodles to the pot or transfer them to a large mixing bowl.
Add a splash of sesame oil to the noodles.
Toss gently until the noodles are lightly coated and separated.
In a medium mixing bowl, combine the remaining sesame oil, soy sauce, Chinese rice vinegar, Chinese sesame paste, smooth peanut butter, granulated sugar, grated ginger, minced garlic, and chile-garlic paste, chile crisp, or chile oil.
Whisk until the sauce is smooth and fully combined.
If the sauce is too thick, add a small amount of cold water, 1 tbsp at a time, until the desired consistency is reached.
Pour the prepared sesame sauce over the cooled noodles.
Toss until the noodles are evenly coated with the sauce.
Add the cucumber sticks and toss gently to combine, or arrange them on top before serving.
Garnish with chopped green onion.
Serve immediately at room temperature or chilled.