Preheat your oven to 375°F and grease a 9 x 5-inch loaf pan or a 10 x 5-inch pan. Line it with unbleached parchment paper for easier removal.

In a small saucepan, melt the butter over low heat along with the milk and vanilla bean paste. Once melted, remove from heat and let it cool slightly.

In a medium bowl, combine the flour, baking powder, orange zest, sea salt, and nutmeg. Set this mixture aside.

Using a stand mixer with a whisk attachment, beat together ½ cup of sugar and the eggs on medium-high speed for about 1-2 minutes until the mixture is pale and fluffy. If you don't have a stand mixer, a hand mixer will work as well. Remember to scrape down the sides of the bowl as needed.

Add half of the dry ingredient mixture to the egg mixture and whisk on low speed until just combined. Gradually whisk in the milk mixture.

Add the remaining dry ingredients and mix on low speed until the batter is smooth.

Peel, core, and quarter the apples. Slice them thinly, aiming for about 1/16-inch thickness, using a mandolin or a sharp knife.

Gently fold the apple slices into the batter with a rubber spatula until they are evenly coated. To prevent browning, it's helpful to slice and coat one apple at a time.

Using a large spoon, ladle a cup of batter into the prepared pan, flattening the apple slices after each addition. Repeat this process until all apple slices are incorporated. You can arrange the top layer of apples decoratively if you like, but don’t stress about it.

Once all the apples are added, tap the pan gently to release any air bubbles. Sprinkle 1 tablespoon of granulated sugar on top.

Bake in the preheated oven for 60-70 minutes, or until the cake is golden brown.

After baking, let the cake cool in the pan on a wire rack for 1 hour. Then, run a knife around the edges and carefully remove the cake from the pan onto the wire rack. Allow it to cool for an additional hour.

Optionally, dust the cooled cake with powdered sugar or serve it with whipped cream. For the best results, cut the cake with a serrated knife. It can be served at room temperature or chilled.