Sweet Potato Hash with Caramelized Onions, Sausage & Eggs

Name: Sweet Potato Hash with Caramelized Onions, Sausage & Eggs
Prep time: 30 min
Total time: 30 min
Cuisine: American
Ingredients: 2 pounds yellow onions (about 2 large or 4 small); 4 tablespoons unsalted butter, ghee, or olive oil, divided; 1 tablespoon kosher salt, plus more as needed; 1 pound uncooked Italian sausage or Mexican chorizo, casings removed; 3 pounds unpeeled sweet potatoes (about 3 large or 6 to 7 small), cut into 1/2-inch pieces; 6 large cloves garlic, minced; Leaves from 2 long fresh rosemary sprigs, minced; Freshly ground black pepper; 8 or more large eggs; Kosher salt; Parmesan cheese (optional)