This salad is meant to be a showcase for apples, so get really good, sweet-tart varieties from the farmers market or your local grocery store. I love Melrose the most, and Mutsu (also called Crispin) second, but Pink Lady is also very good here. Even good ol’ Granny Smith would taste great in the preparation.
Heat the oven to 350 degrees. Spread the peanuts on a large rimmed baking sheet and bake, stirring once halfway through, until golden brown, about 10 minutes. Transfer the nuts to a cutting board and roughly chop while hot. Scrape the peanuts into a small bowl, toss with the sesame oil and season with salt.
Using a microplane zester, remove the zest from one lime and reserve. Juice the two limes and pour the juice in a large bowl. Using a mandoline or sharp knife, very thinly slice the apples, transferring them to the bowl of lime juice as you work. Pour over the black vinegar and add the cilantro leaves, then toss to combine, separating any apple slices that may stick together to ensure every piece is coated in the dressing.
Transfer the apple salad to a large serving platter (or divide among serving plates), spreading it out in an even layer. Season lightly with salt, then sprinkle over the chopped peanuts and reserved lime zest. Using the mandoline or a vegetable peeler, shave large sheets of Parmigiano-Reggiano over the apples. Garnish with more cilantro leaves if you like and serve.
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