Combine first 8 ingredients in a 5-quart electric slow cooker. Cover and cook on LOW for 6 hours.
Place one-fourth of squash 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 squash mixture. Stir in whipping cream, paprika, and cumin. Ladle soup into bowls; top each serving with sour cream and chives, if desired.
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