Clean mushrooms and discard any tough stems. Cut mushrooms into ¼-inch thick slices. Set aside.
In a large heavy bottomed pot or Dutch oven, melt butter until foaming subsides. Add onion and cook until soft but not browned, about 5-8 minutes. Add mushrooms and ½ teaspoon each kosher salt and black pepper. Cook over medium heat, stirring often, until mushrooms have released their liquid and are soft, about 10 minutes.
Add flour and stir to coat the mushroom mixture. Cook for 1 minute. Add sherry and cook for an additional minute, scraping any brown bits from the bottom of the pot.
Stir in chicken or vegetable broth and thyme leaves. Bring to a boil, stirring. (The soup may look, for the lack of a better term, "gloppy" at this point. This is normal! As you stir and the liquid heats, the roux will dissolve.)
Reduce heat to maintain a simmer and cook for 20 minutes, stirring occasionally. Remove from heat.
Transfer 1-½ cups of soup to a blender or food processor and puree until smooth. Stir pureed soup back into the pot.
Stir in heavy cream and season to taste with salt and pepper. Gently warm over low heat, if needed, and serve.
