Preheat oven to 425˚ F. Heat the olive oil in a deep ovenproof skillet over medium-high heat. Add the sausage and cook until browned, transfer to a large bowl with a slotted spoon and set aside.
Heat the olive oil in the skillet and add the onions and mushrooms, cooking until softened and the mushrooms start to brown. Add the garlic and cook for 1 minute. Transfer the onion mixture to the bowl with the sausage with a spoon and set aside.
Melt the butter in the skillet over medium heat, add the flour and cook, whisking, approximately 3 minutes. Whisk in the milk and chicken broth until smooth. Bring the mixture to a simmer, whisking constantly and cook until slightly thickened, about 5 minutes. Whisk in 1/2 teaspoon salt and the nutmeg.
Add the sausage, onion, mushrooms, gnocchi and spinach to the sauce and stir until coated and the spinach wilts. Stir in 1/2 the parmesan cheese and sprinkle the remaining cheese on top. Transfer the skillet to the oven and bake until bubbling and golden, approximately 20 minutes.