Cheesy Radicchio Bake

Ingredients

• unsalted butter, to taste, softened, for greasing the baking dish
• 2 tablespoons olive oil
• 2 medium red onions, thinly sliced
• 1 large head radicchio, cored and sliced into 1/2-inch-thick ribbons
• 2 large cloves garlic, thinly sliced
• 1 tablespoon red wine vinegar
• 3 tablespoons plus 1 1/2 teaspoons kosher salt, divided
• 1 1/2 cups goat cheese, softened and crumbled
• 1 1/2 cups heavy cream
• 3 quarts water
• 1 (16-ounce) box short pasta, such as casarecce or gemelli
• 1/4 teaspoon black pepper
• 1/8 teaspoon nutmeg, freshly grated
• 2 cups fontina cheese, cut into 1/2-inch-thick cubes, divided
• 4 ounces prosciutto, thinly sliced and torn into 1-inch-thick pieces
• 1/2 cup Parmigiano-Reggiano cheese, grated, plus more, to taste, for garnish
• parsley leaves, to taste, for garnish