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In a food processor, puree the strawberries until they are a smooth liquid. PLEASE resist any urges to add water. The thicker the better.
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In a medium bowl, combine the whipping cream, sugar, and strawberry puree.
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Using a stand or electric hand mixer, whip the cream on medium-high speed until stiff peaks form. (Be sure not to over-beat, or you will have strawberry butter instead of strawberry whipped cream. Although, that does sound pretty fantastic as well.)