Melt butter in a large soup pot over medium-high heat; cook mushrooms in butter with 1 pinch salt until the mushrooms give off their juices; reduce heat to low. Continue to cook, stirring often, until juices evaporate and the mushrooms are golden brown, about 15 minutes. Set aside a few attractive mushroom slices for garnish later, if desired. Mix onion into mushrooms and cook until onion is soft and translucent, about 5 more minutes.
Stir flour into mushroom mixture and cook, stirring often, for 2 minutes to remove the raw flour taste. Tie thyme sprigs into a small bundle with kitchen twine and add to mushroom mixture; add garlic cloves. Pour chicken stock and water into mushroom mixture. Bring to a simmer and cook for 1 hour. Remove thyme bundle.
Transfer soup to a blender in small batches and puree on high speed until smooth and thick.
Return soup to pot and stir in cream. Season with salt and black pepper and serve in bowls, garnished with reserved mushroom slices and a few thyme leaves.
