Position a rack in the upper third of the oven and preheat to 450 degrees . Cut the potatoes into 1/2-inch cubes. On a rimmed baking sheet, toss the potatoes with 3 tablespoons olive oil, 3/4 teaspoon salt and 1/2 teaspoon pepper; arrange in an even layer. Roast until golden and crisp at the edges, 25 to 30 minutes.
Meanwhile, in a large pot of boiling, salted water, cook the pasta until al dente. Drain and transfer to a bowl. Add the parsley, butter and remaining 1 tablespoon olive oil and toss. Season with salt and pepper; add the potatoes and toss again.