For the Parmesan crisps: Preheat the oven to 350 degrees F. Line a baking sheet with parchment paper.
Place 6 tablespoon-size mounds of cheese on the parchment a few inches from one another; they will spread as they begin to melt. Bake until the cheese has completely melted, about 5 minutes. Carefully transfer the crisps to a baking rack to cool completely before assembling the salad.
For the green olive dressing: Combine the olive oil, olives, lemon zest and juice, mustard, salt and pepper in a mason jar, twist the lid on tight and shake until emulsified.
For the salad: On a large platter, layer the radicchio leaves with the arugula. Tuck in the citrus pieces. Give the dressing one more good shake and drizzle it over the salad. Garnish with the Parmesan crisps and serve.