Preheat the oven to 350ºF (177°C). Adjust a rack to the middle position. Line a 8 1/2-by-4 1/2-inch (22-by-11-cm) loaf pan with parchment paper so there is some overhanging all sides.
In the bowl of a stand mixer fitted with the whisk attachment, combine the butter and sugar on high speed, scraping down the sides of the bowl occasionally, until pale, very fluffy, and, in the final moments, mousse-like, 8 to 12 minutes. (Alternatively, you can use a hand-held mixer and a large bowl.)
In a medium bowl, whisk together the flour, salt, baking powder, and baking soda.
Gradually add the eggs and egg yolk to the batter, 1 at a time, beating well after each addition.
Switch to your stand mixer’s paddle attachment. With the mixer on low speed, add 1/3 of the flour mixture and mix until just incorporated. Add half the buttermilk and briefly mix until combined. Repeat with another 1/3 of the flour mixture, then the remaining buttermilk, then the last of the flour mixture. Mix just until smooth—do not overmix.
Pour 1/3 of the batter into the prepared bread pan and smooth with an offset spatula or knife. Top the batter with half the apples, overlapping the slices if necessary. Sprinkle the apples with half the cinnamon. Repeat with an additional third of the batter and the remaining apples. Top with the remaining batter and smooth with a spatula.
Bake until the cake is golden brown, starting to pull away from the edges of the pan, and a cake tester inserted into the center comes out clean, 45 to 65 minutes.