In a large bowl, add the vinegar and 1/2 cup of the oil. Add the pine nuts, olives, cherry pepper, capers and lemon zest. Toss the sliced fennel with the lemon juice and a pinch of salt in a small bowl. Combine the fennel with the dressing mixture. Add the fennel fronds and mint. Season with pepper. Let it sit while you cook the pasta.
Add the pasta to the boiling water and cook according to package directions until al dente. Drain, rinse and pat dry on a sheet pan lined with a kitchen towel. In a large bowl, toss with the remaining 2 tablespoons oil.
Add the pasta to the fennel mixture and stir to combine. Season with salt and pepper. Sprinkle the pasta with the cheese. Serve room temperature.