Preheat the oven to 350°F and grease an 8x8x2-inch pan with non-stick cooking spray or softened butter. Line with parchment paper.
In a small bowl, whisk together the flour, salt and baking powder.
Peel, core, and cut the apples into 1/2-inch chunks. Place them in a small bowl and sprinkle with the cinnamon and 2 tablespoons of the sugar and toss with your hands to coat.
In a medium bowl, whisk together the oil and remaining 1 cup sugar. Add the vanilla and eggs and whisk again. Add the cream and whisk a final time.
Using a rubber spatula, fold the dry into the wet in three additions, until just incorporated. Do not over mix.
Transfer the batter to the prepared pan.
Top the cake batter with the apples in a single layer - you may not use all the apple pieces. Sprinkle the cake with the Turbinado sugar.
Bake for 30 to 35 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. The cake will keep wrapped in plastic wrap for three days on the counter.