Blend water, Dari-Free, applesauce, sugar, and vanilla in blender.
Chill in refrigerator until very cold.
Pour into ice cream maker and follow directions. As ice cream mixture turns, slide peaches and rum extract through opening.
If not eaten immediately, freeze in popsicle containers. If you choose to ignore me and freeze in a larger container, I won't say "I told you so" when you discover it's as hard as a rock and you have to babysit the microwave.
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