This makes a coffee-cake like cake. It’s un-iced, and cut into wedges to be served. It's perfect with coffee.
Mix butter and 1 cup sugar on medium-high speed in electric mixer until pale and fluffy, about 3 minutes. Reduce speed to medium-low; mix in egg, milk, and vanilla.
Arrange strawberries on top of batter, cut sides down and as close together as possible. Sprinkle remaining 2 tablespoons sugar over berries.
Bake cake 10 minutes. Reduce oven temperature to 325 degrees. Bake until cake is golden brown and firm to the touch, about 45 - 55 minutes. Let cool in pie plate on a wire rack.