Mix olive oil, Parmesan, garlic, mayonnaise, vinegar, bread crumbs, sesame oil, lemon juice, Worcestershire sauce, Dijon mustard, chili powder, black pepper, basil, hot pepper sauce, salt, oregano, paprika, and cayenne pepper in a shaker or bottle with a lid; shake vigorously. Refrigerate for at least 4 hours to let the flavors combine.