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Core and remove the seeds of the apples and cut them into chunks or slices small enough to fit into a blender, food processor, or bullet.
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In batches (or if processor is large enough), blend the apples with the water until smooth. Pour the mixture into a Dutch oven or pot and add the ground spices.
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Bring the sauce to a simmer and keep covered, cooking for 30 minutes. Let the applesauce cool for 10 minutes.
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Stir in maple syrup and/or honey and grated nutmeg.
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Serve warm or chilled.