Begin by preheating your oven to 350°F (180°C). Grease a 9-inch springform pan thoroughly and set it aside for later use.

In a medium mixing bowl, combine the all-purpose flour, salt, and baking powder. Stir these dry ingredients together just until they’re incorporated and then set the bowl aside.

In a separate, larger bowl, whisk together the granulated sugar, whole milk, melted butter (ensuring it's cool), eggs, egg yolk, and vanilla extract. Whisk the mixture thoroughly until it’s smooth and the egg yolk is fully blended in without any streaks.

Gradually fold the dry ingredients into the wet mixture. Stir gently, making sure not to overmix. Once combined, immediately start preparing the apples. Peel, core, and slice them thinly (aiming for slices around ⅛-inch thick). Folding the apple slices into the cake batter ensures they’re evenly coated.

Pour the batter into your prepared pan, making sure the apples are well-distributed. Sprinkle the top generously with coarse sugar.

Place the cake in the preheated oven and bake for about 1 hour to 1 hour and 10 minutes, or until the top is golden brown and the center is set. Once baked, transfer the cake to a wire rack to cool completely.

When ready to serve, use a spatula to carefully transfer the cake onto a serving plate. Dust with confectioner's sugar just before slicing and serving. Be mindful that the confectioner's sugar will absorb moisture from the apples quickly, so dust it right before serving for the best presentation.

Store any leftovers at room temperature for up to two days, or refrigerate for up to five days to keep the cake fresh.