Preheat the broiler. In a large pot, melt the butter over medium. Add the shallots and garlic; cook, stirring often, until soft, about 5 minutes. Add the flour and nutmeg; cook, stirring often, about 2 minutes. Stir in the cream; cook, stirring often, until the sauce thickens, about 5 minutes. Whisk in half the cheese and 1 tsp. pepper.
Add the spinach. Cook, stirring often, until hot and well combined, about 5 minutes. Transfer to an 8-by-8-inch baking dish. Sprinkle with the remaining cheese. Broil until the cheese browns, 3 to 5 minutes. Sprinkle with more pepper. Let cool 10 minutes.