In a large bowl combine 1 pint of the strawberries and the granulated sugar and with a potato masher mash the berries gently until they release their juices, being careful not to crush them to a pulp. Add the remaining 1/2 pint of berries. Let the mixture stand at room temperature, stirring occasionally, for 1 hour.
In a bowl beat the heavy cream with the sour cream and the confectioners' sugar until it holds a soft shape and beat in the vanilla. Split the biscuits horizontally with a fork, arrange the bottom halves on 4 plates, and spoon the strawberry mixture over them. Top the strawberry mixture with some of the whipped cream and arrange the biscuit tops on the cream. Serve the remaining cream separately.