Arrange potato chips in a single layer on a rimmed baking sheet; top with 1/2 cup Parmesan cheese, dried basil, and garlic.
Bake in the preheated oven until cheese is melted and chips are just starting to brown around the edges, about 4 minutes. Top chips with remaining Parmesan cheese and fresh basil. Drizzle olive oil over cheese layer. Cool and transfer to a serving bowl.