Preheat the oven to 350 degrees and spray an 8x8x2- inch pan with cooking spray. Line with parchment paper.

In a large bowl, whisk together the oil, sugars, and vanilla. Add the egg, and then the yolk, whisking after each. Add the buttermilk and whisk until incorporated.

Sift the flour, salt, baking powder, and baking soda onto a sheet of parchment, and using a rubber spatula, fold the dry into the wet in three additions, until just incorporated. Do not over mix.

Pour the batter into the prepared-pan, scraping the bowl well.

Peel, core, and cut the apples into 1/2-inch chunks. Place them in the now-empty bowl, wiping it with a paper towel first, if you so desire.Sprinkle with the cinnamon and sugar and toss with your hands to coat.

Top the cake batter with the apples in a single layer-you may have some leftover apple pieces. Sprinkle the cake with the Turbinado sugar.

Transfer the cake to the oven and bake for 35 to 40 minutes, rotating the pan after 20 minutes. The cake is done when a tester inserted into the cake comes out with a few moist crumbs.

Bring to room temperature before dusting with confectioners’ sugar and serving along with a dollop of freshly whipped cream, or not, or a scoop of vanilla ice cream, or not.The cake will keep wrapped in plastic wrap for three days on the counter-and some claim it gets better with age.