Remove any tough stems from spinach; wash well and drain thoroughly; put through meat chopper, using the finest blade. (Be sure to catch any juice and mix with the spinach.) In the top part of a double boiler, melt butter and blend in flour.
Add milk gradually and cook, stirring constantly, until mixture is a thick, smooth cream sauce.
Combine spinach with sauce; add to taste with salt, pepper, and nutmeg; cook over hot water for 10 to 15 minutes more.