Preheat the air fryer to 380°F for 3–5 minutes.
Prep the fennel. Trim the stalks and fronds, slice a thin layer off the root end, and halve each bulb lengthwise through the root. Cut a shallow V to remove about two-thirds of the dense core, leaving enough to hold the layers together. Cut each half into ½-inch wedges.
Season. Toss the wedges in a large bowl with the olive oil, kosher salt, and black pepper until every cut surface is coated.
Arrange the wedges in a single layer in the air fryer basket, cut side down, with space between them. Cook in batches if they don't all fit.
Air fry for 6 minutes, then flip each wedge so the opposite cut side faces down.
Air fry for another 5–6 minutes, until the edges are deeply golden and a paring knife slides into the thickest part with no resistance.
Finish and serve. Transfer to a plate, top with Parmesan, lemon zest, or chopped fronds if using, and serve warm.