Have to agree with Granny Moses, proscessing the tougher parts, what a great idea.Think I would have added onion too. LOVE ONIONS in anything.
I had to make one change (not counting the optional seasonings mentioned). I had the tougher parts of the asparagus left over, so once softened and cooled I put them through the food processor. It doesn't look the same, but sure is good. A great soup to have in rainy, cold spring weather.