Slice the chorizo into half-inch thick discs. Heat the olive oil in a large saucepan/Dutch oven over a medium/high heat. Add the sliced chorizo to the saucepan. Cook the chorizo through until golden brown all over and releasing its oil. Remove the chorizo from the pan with a slotted spoon and set aside, leaving the oils in the pan.
Finely dice the onion and celery and dice the squash into small chunks. Crush the garlic. Melt a tablespoon of butter in the saucepan with the chorizo fats. Add the onion, celery, squash, fresh thyme, paprika and garlic. Sweat gently for 5 minutes until tender and fragrant.
Add the chicken stock to the saucepan. Stir well to combine. Bring up to a gentle boil, then reduce to a simmer for 6-7 minutes. The squash should be tender. You may add salt and pepper if desired – this will depend on the strength of seasoning in your stock.
Once the squash is tender, you can blend the soup. Remove from the heat and use a handheld stick blender to carefully blend the soup until smooth. Alternatively, allow the soup to cool a little, transfer to a free-standing blender, and purée until smooth. Divide the soup between 4 individual serving bowls. Top each bowl with the pan-fried chorizo slices. Serve the soup hot with your preferred sides.