Heat a large Dutch oven over medium-high heat. Coat pan with cooking spray. Add mushrooms; sauté 15 minutes or until liquid evaporates. Add shallots; sauté 1 minute. Add 1/4 teaspoon salt and garlic; sauté 1 minute. Remove 1/2 cup mushroom mixture; set aside. Add broth, 3 cups water, chestnuts, and thyme to pan; bring to a boil. Reduce heat and simmer 45 minutes, stirring occasionally. Remove from heat; discard thyme.
Place half of broth mixture in a blender. Remove center piece of blender lid (to allow steam to escape); secure blender lid on blender. Place a clean towel over opening in blender lid (to avoid splatters). Blend until smooth. Pour into a large bowl. Repeat procedure with remaining broth mixture. Stir in remaining 1/4 teaspoon salt, sour cream, and black pepper. Sprinkle with reserved mushroom mixture and bacon.