Maltagliati with Mushrooms and Pea Tendrils

Name: Maltagliati with Mushrooms and Pea Tendrils
Ingredients: 3 tablespoons unsalted butter; 3 tablespoons olive oil; 6 medium clove garlic cloves , lightly smashed; 1 pound fresh porcini, trumpet, or cremini mushrooms (gills removed), cut lengthwise into 1/2-inch-thick slices (about 6 1/2 cups); 1 teaspoon kosher salt; 3 tablespoons sherry vinegar (such as Sanchez Romate Reserva); 12 ounces dried maltagliati pasta (see Note), or fresh lasagna sheets, cut or torn into 1- to 1 1/2-inch squares; 2 ounces Parmesan cheese , grated (about 1/2 cup), plus shaved Parmesan cheese, for garnish; 5 cups lightly packed tender pea tendrils , trimmed and cut into 2-inch pieces