Mushroom Ragu

Name: Mushroom Ragu
Ingredients: 2 ounces dried porcini mushrooms; 1 large red onion, coarsely chopped; 4 medium carrots, coarsely chopped; 4 medium ribs celery, coarsely chopped; 1 pound mixed mushrooms, quartered, such as shiitake and cremini; 6 tablespoons unsalted butter; Coarse salt and freshly ground black pepper; 4 cups crushed tomatoes; 1 sprig fresh basil, coarsely chopped; 1 sprig fresh marjoram, coarsely chopped; 1 sprig fresh rosemary, coarsely chopped; 1 sprig fresh thyme, coarsely chopped; 1 pound rigatoni pasta; 1 cup freshly grated Parmigiano-Reggiano cheese, plus more for serving; Chopped flat-leaf parsley leaves, for serving