Made with gluten-free baking mix and coconut flour, this dessert is a favorite of Lisa Oz, author of The Oz Family Kitchen. She recommends using baking apples like Mutsu, Golden Delicious, and Jonagold.
Position a rack in the center of the oven and preheat to 350°F. Lightly butter a 9-by-2-inch round cake pan.
For the apple-caramel layer, melt butter in a medium skillet. Add brown sugar and maple syrup and cook, stirring often, until sugar has melted and the mixture is boiling. Pour into the prepared pan. Carefully arrange apple slices in two concentric circles in the syrup, overlapping as needed.
For the cake, beat butter in a medium bowl with a hand-held electric mixer on high speed until creamy, about 1 minute. Gradually beat in the sugar and continue mixing, scraping down the sides of the bowl as needed, until light in color and texture, about 2 minutes. One at a time, beat in the eggs, beating well after each addition, followed by the vanilla.
Whisk the baking mix, coconut flour, baking powder, and fine sea salt in another medium bowl. With the mixer on low speed, add the flour mixture to the butter mixture in thirds, alternating with two additions of milk, mixing just until combined after each addition. Scrape batter into cake pan and smooth the top.
Bake until cake springs back when pressed lightly in the center, 35 to 40 minutes. Let the cake cool in pan on a wire cooling rack for 10 minutes. Run a knife around the inside edge of the pan. Place a serving plate over the cake pan. Holding the pan and plate together with a kitchen towel to protect your hands, invert them to unmold the cake. Remove the pan. Cut the cake into wedges and serve, sprinkling flaky salt to taste over each serving.