Melt the butter in a heavy saucepan and stir in the flour.
Cook, stirring constantly, until the flour/butter mixture turns golden.
Pour in the broth slowly, stirring constantly, then add the applesauce, sweet potato, ginger and cinnamon.
Bring the mixture to the boil, then lower the heat until the mixture is simmering gently.
Cook for 5 minutes.
Puree the mixture (either by transferring to a food processor in batches, or using a hand blender in the pot), then return it to the saucepan.
Pour in the milk, warm through gently - and serve.
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