Bring a large pot of salted water to a boil, add pasta, and cook until al dente according to package instructions. Drain and rinse well with cold water.
Meanwhile, combine chopped olives and vermouth, and set aside. For dressing, whisk olive brine, lemon juice, garlic, and Dijon together in a large bowl. Gradually whisk in olive oil until well blended.
Add pasta, olives with vermouth, Parmesan, and parsley, and toss until pasta is well coated. Season with salt and freshly ground black pepper, and gently stir in feta or blue cheese.
Refrigerate for at least 30 minutes before serving. Store in the refrigerator in an airtight container, and serve chilled.
