Preheat oven to 375 degree F.
Line 1 large or 2 small baking trays with a piece of parchment paper.
In a food processor fitted with the steel blade, combine flour, 1/4 cup sugar, baking powder, and salt with a few on/off pulses. Add chilled butter, and process just until combined. With the motor running, pour the cream through the feed tube, stopping just before the dough forms a ball.
Turn out the dough onto a lightly floured surface, and gently knead to form a smooth ball. Do not overwork. Roll out dough to a 3/4-inch-thick round. Using a 3-inch cookie or biscuit cutter, cut out 7 circles. Knead scraps together, roll, and cut out 3 more circles.
Arrange the circles on prepared baking trays, brush tops with cream, and sprinkle lightly with remaining sugar. Bake 5 minutes, reduce the heat to 350 degree F, and bake 15 to 20 minutes longer or until cakes are golden and firm to the touch. Cool on a rack.
To serve, slice each shortbread in half lengthwise. Place a scoop of ice cream or frozen yogurt on bottom half, and cover with top half. Garnish with berries and dust with powdered sugar. Serve immediately.