1/2 cup blanched hazelnuts
2 medium kohlrabi (about 2 pounds total), peeled, thinly sliced on a mandoline
1 tart apple (such as Pink Lady or Crispin), peeled, cored, thinly sliced on a mandoline
1/2 teaspoon finely grated lemon zest
1 tablespoon fresh lemon juice
1 tablespoon white wine vinegar or white balsamic vinegar
1/2 cup torn fresh mint leaves, plus more for serving
1 tablespoon extra-virgin olive oil
2 ounces Pecorino di Fossa or Parmesan, shaved (about 1/4 cup)
Preheat oven to 350°F. Toast hazelnuts on a rimmed baking sheet, tossing occasionally, until golden brown, 10–12 minutes. Let cool, then coarsely chop.
Toss kohlrabi, apple, lemon zest, lemon juice, and vinegar in a medium bowl; season with salt. Add 1/2 cup mint and gently toss to just combine.
Toss toasted hazelnuts and oil in a small bowl to coat; season with salt.
Divide kohlrabi salad among plates and top with seasoned hazelnuts, Pecorino, and more mint.
DO AHEAD: Hazelnuts can be toasted 1 day ahead; store airtight at room temperature.