Preheat the oven to 350°F (175°C) and butter a 9-in (23-cm) deep dish pie pan (or 9-in/23-cm round cake pan).

In a medium bowl, whisk together the flour, baking powder and salt. Set aside.

In the bowl of an electric mixer, beat the butter and 1 cup of the sugar until pale and fluffy, about 3 minutes. Add the egg and vanilla and beat on low speed until well combined. Gradually add the flour mixture, alternating with the milk, and beat on low speed until smooth. (Note: the batter will be thick.)

Transfer the batter to the prepared pan and smooth with a spatula. Arrange the strawberries on top, cut side down, so they completely cover the batter, using more or less as needed. Sprinkle the remaining 2 tablespoons of sugar over the strawberries.

Bake for ten minutes, then reduce the heat to 325°F (165°C) and bake until the cake is lightly golden and a tester comes out clean, about an hour.

Let the cake cool in the pan on a rack. Serve with sweetened whipped cream or vanilla ice cream, if desired.

The cake can be stored at room temperature for several days, loosely covered.