Bring a large pot of water to a boil. Add a generous amount of salt, then cook the pasta until just under al dente, about 1 minute less than the package directions. Drain well.
Remove as much moisture as possible from the pasta. You can return it to the warm pot over low heat for 1–2 minutes, stirring, or pat it dry with paper towels. The drier the pasta, the crispier it will get.
Transfer the pasta to a bowl. Add olive oil, paprika, oregano, garlic powder, onion powder, salt, and black pepper. Toss until evenly coated. Add grated Parmigiano-Reggiano and toss again.
Spread the pasta out in a single layer on a baking sheet or in an air fryer basket. Do not overcrowd.
Bake or air fry at 390°F for 20–25 minutes, turning the pasta every 8–10 minutes so it cooks evenly. The pasta is done when it is golden and snaps when you break it. If it bends, cook a few minutes longer.
While the pasta cooks, make the dressing. In a bowl, whisk together sun-dried tomato oil, olive oil, red wine vinegar, lemon juice, Dijon mustard, garlic, honey, mayo, Italian seasoning, and salt until smooth.
In a large mixing bowl, add olives, sun-dried tomatoes, feta, red onion, cucumber, Parmesan, and pistachios.
Add the hot crispy pasta to the bowl. Pour the dressing over the top and gently toss until everything is evenly coated.
Drizzle with hot honey and sprinkle with extra pistachios. Serve immediately while the pasta is still crisp.