Place a large pot of water over medium-high heat while you cut the potatoes into wedges lengthwise. Just before the water is boiling, remove it from the heat. Add the potatoes to the hot water and blanch them for 10 minutes.
Drain the potatoes and place them on paper towels or a kitchen towel to drain. Once thoroughly dried, transfer the potatoes to a baking sheet.
Preheat the air fryer to 360 degrees F.
Pour the oil over the potatoes and toss they're coated. Sprinkle with garlic, salt, pepper, and Parmesan. Toss to coat.
Transfer the potato wedges to the air fryer basket. (Be sure not to overcrowd them. If needed work in batches for smaller air fryers.) Cook for 8 minutes at 360 degrees F.
Shake the air fryer basket and then cook for 5 minutes at 400 degrees F to really crisp up the potatoes.
When the cooking time is up the potatoes should be crispy and golden brown. Serve warm with extra Parmesan cheese sprinkled on top alongside your favorite dipping sauce.
Notes
If you prefer your potato wedges without the skin, peel the potatoes before cutting them into wedges.