Filling: Rinse the berries under cold water; drain well. Hull and slice the berries; place in a bowl. Sprinkle with 1/3 cup sugar; cover and let stand at room temperature for about 1 hour.
Topping: In a deep, chilled bowl, beat the whipping cream until soft peaks form. Add 2 tablespoons of sugar and vanilla extract, continue beating until soft peaks return. (Do not over beat) Cover and refrigerate until ready to serve.
Preheat the oven to 425 degrees. Set rack at center level. Line a cookie sheet with parchment paper, set aside.
Biscuits: In a food processor (you can use a pastry cutter) combine the flour, baking powder, salt and 3 tablesppons sugar; pulse to mix. Cut butter into about 8 pieces and add to the mixture. Pulse until the mixture resembles coarse meal. Transfer the mixture to a large bowl and make a well in the center. With a fork stir in the cream or milk, just until dough is moist. Be very careful not to overwork. The dough doesn't have to hold together well at this point. Let the dough stand for a minute.
Turn the dough out onto a lightly floured surface. Fold the dough over on itself (knead) 2 or 3 times, until it is holding together and is less sticky. Gently pat the dough into a 6 x 12-inch rectangle about 3/4-inch thick and cut into 8 (3-inch) biscuits with a floured round cutter. Transfer to the prepared cookie sheet. Brush on a little milk or cream and sprinkle tops with some sugar, if desired. Bake for 10 to 15 minutes, until risen and golden brown.
Remove to a platter and split each biscuit horizontally with a serrated knife. Butter the hot biscuits, if desired then top with about 1/3 cup of berry mixture. Replace the tops and top with a tablespoon or so of berries. Serve with a dollop of whipped cream.
Cook's Note: Chill the bowl and beaters in the freezer for 10 minutes before whipping the cream.