Sift the flour, baking powder and salt together in a bowl.
Put the butter and 1 cup sugar in the bowl of an electric mixer fitted with the paddle attachment. Mix on medium-high speed until pale and fluffy, about 3 minutes.
Reduce speed to medium-low, mix in the egg, milk, and vanilla.
Reduce speed to low, gradually mix in the flour mixture.
Transfer the batter to the buttered pie plate.
Arrange the strawberries on top of the batter, cut sides down and as close together as possible. Sprinkle the remaining 2 tablespoons sugar over the strawberries.
Bake the cake for 10 minutes. Reduce the oven temperature to 325 degrees.
Bake until the cake is golden brown and firm to the touch, about 1 hour. Let cool in the pie plate on a wire rack.
Cut into wedges.
The cake can be stored at room temperature, loosely covered, for up to 2 days.