Preheat oven to 350°F.
Grease a 9-inch pie plate and set aside.
In a medium bowl, sift together the flour, baking powder and salt.
In a separate bowl, beat the butter and sugar on medium-high until pale and fluffy, about 3 minutes.
Reduce the mixer speed to medium-low and add the egg, milk and vanilla.
Reduce the speed to low and gradually mix in the flour mixture.
Pour the batter into the pie plate.
Arrange the strawberries on top, cut sides down, as close together as possible.
Sprinkle vanilla sugar over the top of the berries.
Bake at 350°F for 10 minutes.
Reduce the oven temperature to 325°F and bake about 1 hour, until the cake is golden brown and firm to the touch.
Let cool in the pie plate and cut into wedges.
Serve it plain, with whipped cream or with ice cream.