Melt the butter in a large saucepan over medium heat. Add the mushrooms, thyme and the white and light green parts of the scallions, then sprinkle with salt and pepper and cook, stirring, until the mushrooms caramelize and start sticking to the bottom of the pan, about 10 minutes. Scoop out about 1/2 cup mushrooms and transfer to paper towels to drain.
Sprinkle the matcha over the mushrooms in the pan and cook, stirring, for 2 minutes. Pour in the wine and stir to scrape up any browned bits on the bottom of the pan. Pour in the chicken stock and spinach, bring to a simmer and cook, stirring occasionally, until reduced slightly, about 10 minutes.
Remove the soup from the heat and, working in two batches, use a blender to puree the soup until very smooth, about 2 minutes for each batch. Return the pureed soup to the pot, stir in the cream and season with salt and pepper.
Ladle the soup into serving bowls and garnish with the reserved mushrooms and scallion greens.
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.
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