Position two racks in the lower third of the oven. Heat oven to 450*. Line two baking sheets with parchment paper and set aside.
Place the potato wedges in a large bowl. Add the olive oil, salt, and pepper, then toss until evenly coated.
Place the potato wedges on the parchment lined baking sheets, leaving space between each wedge.
Roast 20 minutes. Remove the trays from the oven, flip each wedge, then return the baking sheets to the oven, taking care to switch the positions of the baking sheets to ensure even baking.
While the potatoes finish roasting, prepare the basil butter sauce. Heat a small saucepan over medium high heat. Add the butter and heat until it melts, then foams. Once the foam subsides, add the garlic and sautee, stirring continuously, until fragrant and lightly golden brown, approximately 1 minute. Stir in the basil and remove from heat.
Brush the basil sauce oven the oven fries, then dust with parmesan cheese. Serve immediately. Leftovers can be stored in the fridge for up to three days. Reheat in a skillet over medium heat until re-crisped and dust with fresh basil if available.