Heat the oven to 425 degrees.
In a large bowl, mix together the olive oil, garlic, paprika, 1/2 cup Parmesan, 1½ teaspoons salt and 1 teaspoon black pepper. Set aside.
Slice each potato in half lengthwise. Slice each half in half lengthwise. Then slice each quarter in half lengthwise, so that you have 8 wedges total. Repeat for each potato. Immerse your wedges in a bowl filled with cold water for at least 15 minutes to release extra starch. Dry the wedges before seasoning.
Add the potatoes to the bowl with seasonings and toss with your hands until all the wedges are coated. Arrange on sheet pan so that none of the wedges are touching each other and sprinkle with the remaining ½ cup Parmesan.
Place the sheet pans on the top or center oven rack and bake for 15 minutes. Remove from the oven and flip all the wedges over. Return the pans to the oven and continue baking for 15 minutes more, until the potatoes are golden brown and crispy.
Arrange potatoes on a single sheet pan or on a platter and season with more salt and pepper, to taste. Top with chopped parsley and more Parmesan and serve hot alongside your favorite dipping sauce or condiment.