Someone on here will have a fancier (probably clear) interpretation but I like my soups hearty and rustic. Personally, I'd sweat some onions or shallots, add asparagus cut into 1-inch chunks (tips reserved), saute briefly til slightly browned, then add chicken stock to cover. Allow to come to a simmer, then immersion blend. S&P to taste.
Meanwhile, gently brown asparagus tips and morels in butter til just cooked. Serve asparagus and morels over soup, maybe with a chunk of blue cheese and a few drops of balsamic.