Preheat oven to 350 degrees F. Grease a 10-inch pie plate. (If you must use a 9-inch, don't use all of the batter - the cake will overflow the pan.) Whisk flour, baking powder, and salt together into a medium bowl.

Place the butter and 1 cup of the 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; add egg, zest, milk, and vanilla, and mix well.

Reduce speed to low; gradually add flour mixture. Transfer batter to prepared pie plate. Arrange strawberries on top of batter, cut sides down and as close together as possible. Sprinkle remaining 2 tablespoons sugar over top of cake.

Bake cake for 10 minutes, then reduce oven temperature to 325 degrees F. Continuing baking until 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. Cake can be stored at room temperature, loosely covered, up to 2 days.