Preheat the oven to 450 degrees F.
Fill a 4-quart pot with water and bring to a boil. Season water with salt.
Cut the first 1/2-inch off the top of the heads of garlic to expose all of the cloves. Place garlic heads in the center of a piece of aluminum foil. Sprinkle exposed cloves with salt and pepper, mist with olive oil spray, and then wrap up in aluminum foil. Roast for 45 minutes, and then allow to cool.
Cook pasta according to package directions until al dente. Meanwhile, squeeze cooled roasted garlic cloves into a small saucepan, add chicken stock, and heat over medium heat. With an immersion blender, puree garlic and stock. Simmer until reduced by half. Add half-and-half and simmer until thick. Add Parmesan and blend again with the immersion blender. Taste and adjust seasoning with salt and pepper. Add noodles to pan with sauce and toss to coat. Divide pasta among plates and garnish with parsley.