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Wash and dry all produce.
Quarter lime (for 4 servings, halve 1 lime; quarter remaining). Trim green beans if necessary; cut crosswise into 2-inch pieces. Trim and thinly slice scallions on a diagonal, separating whites from greens. Trim and peel carrots; using a peeler, shave lengthwise into ribbons, rotating as you go, until you get to the cores. Discard cores.
In a small bowl, combine half the bulgogi sauce (all for 4 servings) with juice from half the lime (both lime halves for 4).