Pick the stems off the spinach, and wash it in enough changes of water that no dirt can be seen.
Put the dripping-wet spinach into a saucepan over medium-low heat. Cover the pot and cook until the spinach has wilted completely (about six to eight minutes). If you have a steamer, that's an even better way to cook the spinach.
Remove the spinach to a sieve or colander with small holes. With a spoon, press out the excess water. Place the ball of spinach on a cutting board and chop finely.
Rinse and wipe out the saucepan. Over medium-low heat, melt the butter and add the flour. Make a blond roux, stirring constantly. Before the first hint of browning, remove from the heat and add the milk.
Whisk the milk into the roux to make what looks like runny mashed potatoes. Add the salt, nutmeg, pepper, and spinach. Stir until completely blended.