Prep vegetables. Finely chop leeks, celeriac, parsnips, and shallots. Thoroughly wash asparagus, trim and reserve tips, trim woody bottoms and cut remaining stalk in to 1 inch pieces.

Heat 1/4 cup vegetable oil in a stock pot over medium low heat. Add leeks, celeriac, parsnips, and shallots and sweat in a covered pot for about 15 minutes until almost tender, stirring occasionally. Do not allow vegetables to brown.

Add asparagus and cover pot to sweat for about 30 minutes, stirring occasionally.

Securely bundle herbs in a cloth satchel and toss in to pot with vegetables. Add chicken broth and bring to a simmer. Reduce heat to maintain low simmer. 

Once asparagus is very tender, remove the herbs and taste for salt. Use an immersion blender to make smooth very smooth without any lumps. 

Transfer soup to another large container using a fine mesh strainer to remove all pulp. 

If serving right away, return soup to heat and whisk in cream if desired, about 1/4 cup per serving, and serve hot. 

If reserving to serve later, transfer to soup to refrigerator. Bring up to temp on stove top and whisk in cream, about 1/4 per serving, prior to serving.