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In a large soup pot, melt the butter. Add three-fourths of the sliced mushrooms, the shallots and garlic and cook over moderately high heat, stirring frequently, until the mushroom liquid has evaporated and the mushrooms are lightly browned, 30 minutes.
Add the chicken stock, water, thyme and parsley and bring to a boil, scraping up any browned bits stuck to the bottom of the pot. Cover and simmer over moderately low heat for 1 hour. Strain the mushroom broth into a heatproof bowl, pressing hard on the solids with the back of a spoon. Discard the solids and wipe out the soup pot.
Return the broth to the pot. Add the remaining sliced mushrooms, bring to a boil over high heat and cook them for 2 minutes. Using a slotted spoon, transfer the mushrooms to a blender. Add 1 cup of the broth and puree until smooth. Return the mushroom puree to the soup and stir in the heavy cream, soy sauce and cornstarch mixture and bring to a simmer. Cook just until slightly thickened, about 5 minutes. Season with salt and pepper.
In a large skillet, cook the chorizo over moderate heat until the fat is rendered, about 5 minutes. Drain the ground chorizo on a paper towel. Wipe out the skillet and melt the butter. Add the quartered mushrooms and cook over high heat until lightly browned, about 6 minutes. Add the scallions and chorizo and cook just until the scallions are softened, about 1 minute. Mound 1/4 cup of the garnish in the center of 10 soup bowls, ladle the soup all around and serve.
A fruity, earthy Rioja with rich flavors will echo the mushrooms in this soup.