Preheat oven to 425 F and set one rack in the upper third section.
Heat a large, oven safe skillet or Dutch oven over medium and melt 2 tbs butter. Add mushrooms to skillet along with the nutmeg. Cook, stirring frequently, until some of the liquid has been released and cooked off, about 10 minutes.
Add the white wine and shallot to the skillet, and continue cooking until most of the wine has evaporated. Remove mushrooms to a plate.
Melt 2 tbs butter in the skillet then add the flour. Whisking constantly, cook about 3 minutes to lightly toast the flour. Add milk and chicken broth, and whisk until smooth. Simmer to thicken, about 5 minutes, then stir in cardamom and any desired salt and pepper.
Return the mushrooms to the skillet, and add the chicken, gnocchi, and spinach. Stir to mix in and coat with sauce, and continue to cook until the spinach wilts.
Sprinkle on about 1/2 to 3/4 the Parmesan, then transfer to the oven. Bake until bubbling and, about 20 minutes. To brown, turn on the broiler and bake another 3 minutes.
Serve warm, with freshly cracked pepper and a sprinkling of Parmesan.