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Melt butter in a large pot over medium heat.
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Once butter foams, add onion, and season generously with salt.
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Cook, stirring occasionally, until onion is tender but not browned, about 5 minutes.
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Add rutabaga and broth, bring to a boil, then reduce heat to low and simmer until rutabaga is tender when pierced with a fork, about 30 minutes.
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Add half-and-half, paprika, and pepper and stir to combine.
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Allow soup to cool slightly, then purée in a blender until smooth. (You will have to do this in batches.)