Preheat the oven to 400 degrees F.
Place the gnocchi in a lightly greased 9-by-13-by-2-inch baking dish. Set aside.
In a medium saucepan, whisk together the cream, chicken broth, and the flour over medium heat. Continue whisking until the cream is simmering and thickened, about 5 minutes. Add the salt, pepper, and nutmeg and stir to combine. Add the spinach and toss to coat in the cream. Pour the cream and spinach mixture evenly over the gnocchi and gently spread the spinach out to cover. Crumble the goat cheese over the spinach. Sprinkle with parmesan cheese.
Bake until the top is golden in places, about 30 minutes.