Preheat the oven to 350 degrees and butter a deep dish pie pan.
In a small-ish bowl, whisk together the dry ingredients: flours, baking powder and salt. In the bowl of a stand mixer (or you can use a hand-held mixer), add the butter and granulated sugar and beat until pale and fluffy, about 3 minutes.
Add the egg, buttermilk and vanilla and stir just until combined. Add the dry ingredients to the wet ones and mix until smooth.
Pour the batter into the pie pan. Arrange the strawberries on top in a single layer. They will end up very close together but that's okay because as it bakes the dough will come up in between them.
Sprinkle the Turbinado sugar over the top of all. Bake the cake for 10 minutes at 350 and then reduce the tmperatureto 325. Bake for about 50 to 60 more minutes,, until a toothpick inserted in the batter comes out clean (try to avoid the strawberries when you do this!)
Let cool in the pan and cut in wedges to serve.