Melt butter in a large saucepan over medium heat. Whisk in flour, and cook until the mixture turns a darker yellow color, about 5 minutes. Stir in the mushrooms, and cook for 2 minutes.

Whisk in the sherry, chicken broth, and milk, then add the spinach, green onion, nutmeg, salt, and pepper. Bring to a boil over high heat, whisking constantly, then reduce heat to medium low, and simmer until the spinach is tender, 15 to 20 minutes.