Melt the butter over medium-high heat. Add the flour and cook, stirring constantly, until smooth, about 30 seconds. Add the milk and nutmeg and whisk constantly until the mixture thickens, about 1 minute.
Heat the oil in a medium saute pan over medium-high heat. Add the garlic and onions and cook until soft, about 2 minutes. Add the chopped spinach and cook until warmed through. Stir the spinach into the milk mixture. Top with the cheese and serve.