Step 1

Bring a large pot of water to a boil, add the noodles, and cook until just barely tender, 5 to 6 minutes, or according to the package instructions. Drain well. Toss them with the sesame oil to coat. Cover and refrigerate.

Step 2

Meanwhile, in a large bowl, thin the sesame paste by stirring enough water into the paste to achieve the consistency of thick cream. Whisk together the vinegar, soy sauce, and sugar. Add the mixture to the sesame paste. Stir in the garlic, three quarters of the scallion, and the ginger.

Step 3

Just before serving, toss the chilled noodles with the sauce. Garnish with the remaining scallion and drizzle with the chili oil, if using.