Cook the noodles: Bring a large pot of salted water to a rolling boil — you should see big, steady bubbles breaking the surface. Drop in the udon noodles and cook according to the package instructions, usually 6–8 minutes. Stir once halfway through to prevent sticking; the noodles will turn from opaque to a glossy, translucent white when they're done. Drain into a colander and rinse under cold running water until the noodles feel cool to the touch — this stops the cooking and removes excess starch. Shake the colander well to get rid of as much water as possible, then set aside.

Make the dressing: While the noodles boil, grab a medium mixing bowl. Add the peanut butter, soy sauce, toasted sesame oil, rice vinegar, honey, grated garlic, and grated ginger. Whisk vigorously with a fork — the mixture will look thick and clumpy at first, almost like a stiff paste. Add the warm water, one tablespoon at a time, whisking after each addition. The dressing will loosen into a smooth, pourable consistency that coats the back of a spoon. Taste it: you're looking for a balance of salty, nutty, and slightly sharp. Adjust with a splash more vinegar if it feels too rich.

Prepare the vegetables: Using a vegetable peeler, run it down the length of the carrot to create thin ribbons — they should curl slightly and feel pliable. Slice the cucumber in half lengthways, then cut each half into thin half-moons about half a centimetre thick. Slice the spring onions on a sharp diagonal so you get pretty green and white rings. These vegetables add crunch and freshness to balance the rich dressing.

Combine everything: Tip the cooled, drained noodles into the bowl with the dressing. Add the carrot ribbons, cucumber slices, and most of the spring onions (reserve a few for garnish). Using tongs or two large forks, toss everything together gently but thoroughly. Lift the noodles from the bottom and fold them over the top until every strand is glossed with dressing — you should see the sauce clinging evenly, with no dry patches of noodle left.

Finish and serve: Transfer the salad to a serving platter or individual bowls. Sprinkle over the toasted sesame seeds, the reserved spring onions, and a scattering of fresh coriander leaves if using. The contrast of the pale noodles against the orange carrot ribbons and green cucumber makes this dish look as good as it tastes. Serve immediately for a cold, refreshing dinner, or cover and refrigerate for later.