Put a large pot of lightly salted water on to boil. Toast walnuts in a small skillet over medium heat, stirring, until fragrant, 3 to 4 minutes. Transfer to a plate to cool.
Tear bread into large pieces and pulse in a food processor to form fine crumbs. Add parsley, garlic and the walnuts and pulse until finely chopped, scraping down the sides as needed. Add yogurt and oil; process until smooth. Season with salt and pepper.
Cook pasta until just tender, 8 to 10 minutes, or according to package directions. Drain and place in a warmed large shallow bowl. Toss with pesto until well coated. Sprinkle with Parmesan and serve.