Preheat oven to 425°F (220°C). Line a large baking sheet with parchment paper. Cut each potato in half lengthwise, then cut each half into 3-4 wedges, depending on size, for a total of 8-12 wedges per potato.
In a large bowl, toss the potato wedges with olive oil, garlic powder, oregano, paprika, 1 tsp salt, and 1/2 tsp black pepper until evenly coated.
Arrange the wedges in a single layer on the prepared baking sheet, ensuring they are not touching. Bake for 15 minutes.
Flip each wedge over. Return to the oven and bake for another 12-15 minutes, or until deeply golden brown, crispy on the outside, and tender inside.
While the wedges bake, combine the melted butter and minced garlic in a small bowl. Let it sit for 5-10 minutes to infuse. In a separate small bowl, mix the grated Parmesan and chopped parsley.
As soon as the wedges come out of the oven, transfer them to a large, clean bowl. Pour the garlic butter over them and toss gently to coat. Immediately add the Parmesan-parsley mixture and toss again until the cheese starts to melt and cling to the wedges.
Transfer the wedges to a white serving plate. Garnish with an extra sprinkle of Parmesan and parsley. Serve immediately with ranch or aioli on the side.