Wash spinach thoroughly; drain and chop coarsely. (If you're using frozen spinach, defrost it and drain thoroughly.).
Place a sieve or strainer over a large bowl; set aside.
In a large saucepan or soup pot, bring broth to a boil. Add spinach. Simmer 5 minutes, then pour into sieve or strainer, catching the stock in the bowl. Press the spinach with a spoon to remove as much liquid as possible. Set the stock aside. Chop the spinach very fine. (this step not necessary if using frozen spinach).
Melt the butter in the saucepan or soup pot. Remove pan from heat and stir in the flour. Using a whisk, slowly add the hot broth, mixing well. Return pan to heat and bring broth to a boil, stirring constantly.
Add spinach, salt, pepper, and nutmeg. Cover pan, reduce heat, and simmer 5 minutes, stirring occasionally.
Serve soup garnished with slices of hard-boiled egg.