Preheat the air fryer to 400°F (200°C). Have a wire rack or a plate ready to hold breaded cauliflower pieces.
Cut the cauliflower into florets.
In one large bowl or shallow dish, lightly beat the 2 large eggs. In a second bowl or shallow dish, combine the 1 cup panko breadcrumbs and 1 cup seasoned fine breadcrumbs.
Working one floret at a time, dip each cauliflower floret into the beaten eggs, then press it into the breadcrumb mixture to coat. Place each breaded floret on the wire rack or plate. Repeat until all florets are breaded. You will likely need to cook in 1–2 batches depending on your air fryer size.
Arrange a single layer of breaded cauliflower florets in the air fryer basket. Spray the tops lightly with olive oil (or another oil spray). Cook at 400°F for 15 minutes. If your air fryer model benefits from turning or shaking food for even browning, flip or shake the florets about halfway through cooking. Remove cooked florets with tongs to a plate and repeat with remaining batches.
While the cauliflower cooks, prepare the kale: place the chopped kale in a large bowl, drizzle with 1 to 2 tablespoons olive oil, and massage the leaves with your hands for 2–3 minutes until they soften and become less bitter. Let the massaged kale sit for about 10 minutes.
Make the bang bang sauce by whisking together 1/2 cup mayonnaise, 4 tablespoons sweet chili sauce, and 3 teaspoons chili garlic sauce. Stir in the 3 tablespoons fresh chopped chives.
When all cauliflower is cooked, drizzle the bang bang sauce over the hot florets and toss gently to coat.
Dress the kale salad: squeeze the juice of 1 lime over the massaged kale, season with kosher salt and pepper to taste, then toss in 1/3 cup shaved parmesan and 1/4 cup pickled onions (or sliced red onion).
Divide the kale salad among plates or a serving bowl, top with the bang bang cauliflower, and serve immediately.