Cold Sesame Noodles

Steps

1. Make the sauce. Stir the sesame paste in its jar to work back in the oil that has risen to the top, then put 4 tablespoons in a bowl with the peanut butter, sugar, soy sauce, and black vinegar. Whisk: the mixture thickens and turns grainy, which is normal.
2. Add 80 ml (1/3 cup) of the hot water, 1 tablespoon at a time, whisking after each addition. The sauce seizes up at first, then suddenly loosens and turns smooth and glossy. Stop when it's like a thick pourable cream that coats the back of a spoon. Save the rest of the water for later.
3. Grate the garlic and ginger straight into the sauce, then add 1 tablespoon of sesame oil and 2 tablespoons of chili oil. Taste: it should seem a little too salty, too sweet, and too tart, because the cold will mute it. Cover and refrigerate.
4. Bring a large pot of water to a boil, unsalted: the soy sauce does the seasoning. Add the noodles, stir for the first 30 seconds so they don't stick, and cook according to the package, usually 4 to 6 minutes, until tender all the way through with no white core or bite.
5. Drain and rinse right away under cold running water, rubbing them between your hands for 1 minute, until they're cold and no longer sticky at all. Let them drain for 5 minutes, shaking the colander now and then: leftover water would thin the sauce.
6. Put the noodles in a large bowl and toss with the rest of the sesame oil. At this point they keep for up to 2 days in a sealed container in the fridge.
7. Halve the cucumber lengthwise and scoop out the seeds with a teaspoon if they're large. Cut two-thirds of it into thin 2-inch (5 cm) matchsticks and the last third into thin rounds. Slice the scallions on the bias, cut the chile into thin rounds, and cut the lime into wedges.
8. When you're ready to serve, take out the sauce: the cold will have thickened it, so loosen it with the rest of the water, reheated, until it pours again. Pour it over the noodles and lift and toss with tongs for 1 minute, until every strand has a glossy beige coating. Add the cucumber matchsticks and half the scallions and toss again.
9. Divide among shallow bowls. Top with the cucumber and chile rounds, the rest of the scallions, and the sesame seeds. Drizzle with the remaining chili oil and set a lime wedge on the edge of each bowl to squeeze over at the table.