While the squash is cooking, place a 12-inch skillet over medium-high heat and add the Italian sausage. Break up the sausage with a spatula so it can evenly brown and no large chunks remain. When half of the sausage is browned, add in the diced onions and sliced mushrooms. Continue cooking until the sausage is fully cooked and the onion and mushrooms are soft. Remove from heat and set aside.