Cheesy Baked Pasta with Radicchio

Name: Cheesy Baked Pasta with Radicchio
Ingredients: 2 tablespoons olive oil; 2 medium-size red onions, thinly sliced; 1 large head radicchio, cored and sliced into 1/2-inch-thick ribbons; 2 large garlic cloves, thinly sliced; 1 tablespoon red wine vinegar; 3 1/2 tablespoons kosher salt, divided; 6 ounces softened goat cheese, crumbled (about 1 1/2 cups); 1 1/2 cups heavy cream; 3 quarts water; 1 pound uncooked short pasta (such as gemelli, casarecce, or strozzapreti); 1/4 teaspoon black pepper; 1/8 teaspoon freshly grated nutmeg; 8 ounces fontina cheese, cut into 1/2-inch cubes (about 2 cups), divided; 4 ounces thinly sliced prosciutto, torn into 1-inch pieces; Unsalted butter, softened, for greasing baking dish; 2 ounces Parmigiano-Reggiano cheese, grated (about 1/2 cup)