Cheesy Sausage and Sage Stuffing

Name: Cheesy Sausage and Sage Stuffing
Ingredients: 2 tablespoons unsalted butter, plus more; 1 medium boule sourdough, cut into 1-inch pieces (9–10 cups), dried out overnight; 2 tablespoons olive oil; 1 pound sweet or spicy Italian sausage, casings removed; 2 large onions, finely chopped; 3 celery stalks, chopped; ¼ cup finely chopped sage; Kosher salt, freshly ground pepper; 1 cup dry white wine; 2 large eggs, beaten to blend; 1 cup low-sodium chicken broth; 2 cups half-and-half; 1 pound aged cheddar, grated (about 5 cups), divided