Cook onions: Cook onions in 4 tablespoons butter in a large stockpot over medium heat until soft, 4 to 5 minutes.
Add flour and cook: Stir in flour and cook over low heat for 4 minutes without browning.
Add stock: Add the stock, blending it completely with the flour.
Add herbs and simmer: Add the parsley, bay leaf, and thyme, and simmer for 20 minutes. Strain into a second pot.
Cook cremini mushrooms in a skillet: In a large skillet, heat remaining 4 tablespoons butter over medium heat. Add the cremini mushrooms and season with salt. Cook until softened.
Add other mushrooms and cook: Add the shiitake and oyster mushrooms. Season with salt and lemon juice and cook until mushrooms are deep golden brown, 8 to 10 minutes.
Reheat stock mixture and whisk in yolks and cream: Reheat stock mixture to a simmer. Whisk the egg yolks and cream until blended.
Add cream mixture to soup carefully: While whisking, slowly add a cupful of the hot soup into the cream mixture and add back to the soup and heat to just below a simmer (if the soup simmers, the yolks will curdle).
Add mushrooms to soup: Add the cooked mushroom mixture and stir to combine. Serve garnished with parsley.
