In a Dutch oven or other large pot, fry the chopped bacon until crisp. Remove bacon and drain on paper towels. Set aside, crumble when cool enough to handle.
In the Dutch oven, reserve 1-2 tablespoons of bacon fat; cook the onion in the reserved bacon fat until translucent. Stir as needed to keep the onions from browning.
Add the chicken stock and the squash to the onions in the Dutch oven. Simmer until squash is tender.
Remove from heat. Working in batches, in a blender or food processor, puree the squash, onions, and fresh basil. Note: When working with hot products, make certain that the blender lid is vented in order to prevent a steam build-up hazard. A good immersion blender may also be used to puree the ingredients.
Return the puree to the Dutch oven and stir in the thyme, salt, pepper, smoked paprika, and sour cream (if using) until well blended. Over medium heat, warm the soup until steam begins to rise, stirring as necessary.
Once the soup is hot, add the cheese and stir until cheese has melted.
To serve, sprinkle soup with smoked paprika, cheese, minced basil, and bacon crumbles.