Gently wash the blackberries and remove any stems or leaves. Place half of the blackberries in a saucepan with 1/4 cup of the sugar. Cook over medium heat for about 5-7 minutes, or until the blackberries have softened and released their juices. Stir occasionally to prevent sticking. This creates a lovely blackberry compote.
Remove the saucepan from the heat and let the blackberry mixture cool slightly. Then, use a blender or food processor to puree the cooked blackberries until smooth. If you prefer a smoother fool, you can strain the puree through a fine-mesh sieve to remove the seeds. Set the blackberry puree aside to cool completely.
In a large bowl, combine the heavy cream, yogurt, vanilla extract, and the remaining 1/4 cup of sugar. Use an electric mixer to whip the cream mixture until soft peaks form. Be careful not to overwhip, or the cream will become grainy.
Now for the fun part! In individual glasses or a large serving bowl, layer the blackberry puree, whipped cream mixture, and the remaining fresh blackberries. Repeat the layers until all the ingredients are used up, finishing with a layer of whipped cream and fresh blackberries on top.
Cover the Blackberry Fool and chill in the refrigerator for at least 30 minutes before serving. This allows the flavors to meld together and the fool to set slightly. Garnish with fresh mint sprigs, if desired, and enjoy!