Place cashews in a bowl, cover with water, and soak for at least 2 hours. Drain and place in a blender container along with barely enough water to cover the nuts. Process until smooth, 1 to 2 minutes.
To make the chocolate mixture, heat the cashew cream, white chocolate, and vanilla extract in small saucepan over low heat, stirring regularly, until the chocolate has melted. Divide berries among 12 paper-lined medium-sized muffin cups. Pour chocolate mixture evenly over the berries and place in the freezer until solid.
Unmold chocolate berry cups and place in a zip-top bag for storage in the freezer until ready to serve. If not using paper liners and you have trouble unmolding the contents, try placing the bottom of the muffin tray in warm water for several seconds, being careful not to thaw the contents.