Add the chickpeas, 1 tablespoon olive oil, and half of the paprika to a medium bowl, tossing to combine. Season with salt and pepper.
Add the chickpeas to the air fryer basket at 390F for 8 to 10 minutes, shaking halfway through. Once crisp, remove them from the air fryer.
Meanwhile, toss the remaining 2 tablespoons of oil, paprika, garlic powder, turmeric, and cauliflower in the bowl.
Add the cauliflower to the air fryer once the chickpeas are done. Air fry at 390F for 16-18 minutes, shaking halfway through. Once cooked, top the hot cauliflower with ¼ cup parmesan.
In a large bowl, toss the crispy chickpeas, cauliflower, arugula, parsley, and remaining parmesan cheese. Squeeze lemon juice overtop, and toss before serving.