1. Melt butter in a saucepan. Sweat chopped shallots in melted butter.
2. Cut mushrooms and shiitakes into quarters and add them to the shallots, then add chicken stock. Season with salt and pepper, Bring to the boil and simmer for 30 minutes.
3. Carefully skim any fat or impurities from the surface while it cooks.
4. Remove saucepan with mushrooms from heat. Puree the cooked mushrooms using a hand held immersion blender or food mill. The puree should be very smooth.
5. Strain the puréed mushroom mixture through a china cap sieve into another saucepan. Place saucepan on stove top over low heat.
6. Whisk the 1-3/4 cup of cream into the pureed mushroom mixture, adjust seasoning.
7. Add 3/4 ounce of butter, whisk to incorporate.
8. Prepare the liaison. In a separate bowl, whisk the egg yolks and cream.
9. Whisk in a ladleful (8 ounces) of the mushroom soup into the liaison and then whisk in the remaining soup. Pour the mixture into a saucepan and stir with a spoon over medium heat until the soup thickens enough to coat the back of the spoon. (Do not let the soup boil or it will curdle.)
10. Put the dried morel mushrooms through a mixer to make a powder, then pass the powder through a sieve. To serve, pour the mushroom soup into a bowl, add three tablespoons of whipped cream and sprinkle the top with the morel mushroom powder.
*Note: Cep (porcini) or other seasonal wild mushrooms can be used in place of shiitake mushrooms.