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Step 1
Make the veloute. Heat the stock to a bare simmer. In another pot, heat the butter until frothing and stir in the flour. Stirring all the while, let this cook for a few minutes over medium heat. Do not let it brown. Whisk the hot stock into the roux and let this simmer for 20 minutes, stirring often. You want it to slowly cook down by at about 1/4 and be silky looking.
Step 2
While the veloute is simmering, make the mushroom base. Mince the mushrooms and shallots fine and sweat them in a saute pan over medium heat with a touch of salt. Cook, stirring often, until the shallots are translucent and the mushrooms give up their water.
Step 3
Crumble the saffron into the brandy and add it to the mushroom base. Turn the heat up to high and toss or stir to combine. Cook until the brandy is nearly gone. Buzz the mushroom base into a puree in a food processor. OPTIONAL: If you want a truly refined French soup, push this puree through a fine-mesh strainer.
Step 4
When the veloute is ready, add the mushroom puree and stir well to combine. Cook this at a bare simmer for 10 minutes. OPTIONAL: If you want a mushroom garnish, slice a few chanterelles lengthwise and sear them in an dry pan until they give up their water and brown.
Step 5
Beat together the egg yolks and cream, then ladle — a little at a time — some soup base into the egg-cream mixture. This is called a liaison, and you are tempering the eggs with the hot stock slowly, so they do not congeal. Once you have 3 or 4 ladles of soup into egg-cream mixture, pour it all back into the soup and simmer. Do not boil or it will break. OPTIONAL: Put this soup through the fine-mesh strainer again to remove any lumps and return to low heat.
Step 6
To finish the soup, turn off the heat and whisk in the remaining butter. Serve with the seared mushrooms in the center, with crusty bread and white wine. Enjoy decadence.