Butternut Squash and Wild Mushroom Stuffing

Name: Butternut Squash and Wild Mushroom Stuffing
Prep time: 20 min
Cook time: 50 min
Total time: 1 h 10 min
Cuisine: American
Ingredients: 2 tablespoons olive oil; 1/2 small onion (finely diced); 4 cups cubed butternut squash; 1 tablespoon brown sugar; 3-4 cups mixed mushrooms (sliced if large); 2 cloves garlic (minced or grated); 2 tablespoons fresh sage; 2 tablespoons fresh oregano; 1 tablespoon fresh thyme; 2 tablespoons balsamic vinegar; 1 teaspoons salt + pepper; 8 tablespoons ( 1stick) butter; 3 1/2-4 cups low sodium chicken or turkey broth; 3 eggs; 12 cups cubed day old sourdough bread ((about 1 loaf)); 1 cup Asiago cheese (grated)