Wash the acorn squash thoroughly. Use a sharp knife to cut the squash in half from stem to point. Scoop out the seeds and stringy pulp with a spoon. Slice the squash into 1-inch thick wedges or crescents. You can leave the skin on as it becomes tender and edible after cooking.
In a large mixing bowl, combine the olive oil, maple syrup, cinnamon, nutmeg, salt, and pepper. Add the squash wedges to the bowl and toss them until every piece is evenly coated with the spice mixture.
Preheat your air fryer to 400°F (200°C) for a few minutes. Place the seasoned squash wedges in the air fryer basket in a single layer. Make sure they are not overlapping too much to ensure the air can circulate around each piece for even browning.
Cook the squash at 400°F for 15 to 20 minutes. Halfway through the cooking time, pause the air fryer and shake the basket or use tongs to flip the wedges. The squash is done when it is fork-tender and the edges are golden brown and slightly crispy.
Remove the squash from the air fryer and transfer it to a serving platter. If desired, drizzle with a tiny bit more maple syrup or a sprinkle of fresh parsley before serving warm.