If using fresh spinach, bring a large pot of water to a boil. Add the spinach in batches and cook for just 1 minute until wilted. Drain in a colander, then transfer to a clean kitchen towel. Gather the towel around the spinach and squeeze as hard as you can until very little water comes out. Roughly chop the spinach and set it aside. If using frozen spinach, thaw it completely and squeeze it the same way in a kitchen towel until it is nearly dry. This step is critical: watery spinach will thin out the sauce.

Melt the butter in a large saucepan over medium heat. Add the diced onion and cook, stirring often, for 4 to 5 minutes until softened and translucent. Do not let it brown.

Sprinkle the flour over the cooked onion and stir constantly for about 1 minute to cook out the raw flour taste. The mixture will look like a thick paste, which is exactly right.

Pour in the warm milk in a slow, steady stream while whisking constantly. Keep whisking over medium heat for 3 to 4 minutes until the sauce thickens and coats the back of a spoon. It should be smooth with no lumps. If you see small lumps, keep whisking over heat and they will smooth out.

Reduce the heat to low. Add the grated Gruyere and stir until it is fully melted and the sauce is glossy. Stir in the nutmeg, salt, and white pepper.

Add the squeezed, chopped spinach to the sauce and stir well to combine. Let everything simmer together over low heat for 3 to 5 minutes, stirring frequently, until the spinach is fully incorporated and the mixture is thick and creamy. Taste and adjust salt if needed, then serve hot.