Core and slice the apple; toss in 1 tablespoon of the lime juice. Place carrots and cabbage in a large bowl and cover with boiling water. Let sit 5 minutes; drain and cool slightly. Whisk together oil, shallot, the remaining lime juice, salt, and cumin; add freshly ground pepper to taste. Toss carrots, cabbage, and apple in a large bowl with dressing, mint, and sunflower seeds. Serve at room temperature or chilled.
I followed the recipe exactly. There is way, way too much carrot -- it totally overwhelms the slaw. I saw no advantage to soaking the vegetables in hot water; even after thoroughly draining, water ended up diluting the dressing. The dressing itself was excellent, however. The sunflower seeds added a surprising flavor. Word of warning: the salad is better eaten right away; it lost its intensity the longer it sat. Does not keep well. Even though it has potential, I doubt I'll make again.
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