Simmer asparagus ends in water till tender, about 15 minutes. Let cool and then put Asparagus and cooking water in food processor and run till liquified.
Put pulp in a regular strainer, set over the pot and using the back of a spoon press out all the pulp. Keep working pulp till all that is left is the tough outer skin of the ends. Discard outer skin.
Add chicken broth to the asparagus pulp. Mix together the milk and flour to make a paste and add to the vegetable broth ingredients. Return the pot to stove and stirring over medium, heat cook the soup till it thickens. Add salt and pepper to taste. Grate fresh nutmeg over soup. Remove from heat.
When serving, the soup will be quite thick so use either milk, cream, or sour cream to thin to desired thickness.