Preheat oven to 375° and line sheet pan with parchment paper.
Place prosciutto in a single layer and bake until crisp, 15.
In a large bowl, massage kale with oil and lemon juice using your hands.
Season with lemon zest, sea salt, and pepper.
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Using a vegetable peeler, shave 1/2 cup Pecorino Romano over salad and gently fold in cheese and apples.
Transfer salad to platter.
Break up prosciutto pieces by hand and crumble on top of salad.
Finish with pepper and remaining 1/4 cup Pecorino; drizzle with balsamic vinegar.