Arrange a rack in center of oven; preheat to 400°. Set a wire rack in a large rimmed baking sheet. In a large bowl, toss wings with oil; season with salt and black pepper.
Transfer wings to prepared rack and bake until golden and crispy, about 50 minutes.
In a large bowl, stir garlic, Parmesan, butter, parsley, and red pepper flakes. Add wings and toss until coated.
Transfer wings to a platter. Sprinkle with Parmesan. Serve with Caesar dressing alongside.
