Boil freshly made or store-bought hand-pulled noodles until cooked, then drain and set aside in a large bowl.
Cut cucumber into thin strips for garnish.
Crush garlic and mince it into fine pieces.
Gradually mix water into sesame paste (about 2 tablespoons) to thin it, then stir in one tablespoon of salt until smooth.
Combine the noodles, cucumber strips, thinned sesame paste, and minced garlic in the bowl. Add 2 tablespoons of vinegar, 2 tablespoons of light soy sauce, and 1 tablespoon of sesame oil, mixing thoroughly.
Heat 2 tablespoons of peanut oil in a large iron spoon over medium-low heat until it reaches 70-80% hot (slightly smoking). Add a small handful of Sichuan peppercorns, turn off the heat immediately, and let the residual heat infuse the oil with flavor. Strain out the peppercorns and mix the infused oil into the noodles.
Sprinkle with crushed nuts such as peanuts, cashews, or white sesame seeds for enhanced taste.
Adjust salt to preference if a stronger flavor is desired.
Extremely delicious—expect to enjoy at least two bowls!