Preheat oven to 350°F (176°C). Coat a 9-inch springform pan with butter and dust with flour, tapping out any excess.
In a bowl of a stand mixer fitted with the paddle attachment, or in a bowl using a hand mixer, beat the butter until creamy. With the mixer running, slowly add the sugar and continue beating until fluffy.
Plop in the egg and beat until combined, then mix in the vanilla.
Whisk the flour, baking powder, baking soda, and salt together in a large bowl. Alternate adding the flour mixture and buttermilk to the bowl in 3 batches, beating after each addition.
Pour the batter into the prepared pan and smooth the top with a spatula.
Starting at the outside of the pan, stand the apple slices on their narrow end in the batter to form a circle, fitting them as snugly as you can. Fill in the center of the circle with as many slices as will fit.
Bake until a toothpick inserted into the cake--not the apples--comes out clean, 50 to 60 minutes. Transfer the pan to a wire rack, unlatch the pan, remove the adjustable sides, and allow the cake to cool.
Sprinkle confectioners’ sugar over the cake just before serving, if desired.