Preheat the oven to 325 degrees F and place an oven rack in the center position. Spray a 9x5 inch loaf pan with baking spray (or use butter) and line the bottom with parchment paper.
Whisk the flour, salt and cinnamon together and set aside.
In a stand mixer with the paddle attachment, cream the butter and sugar together on high speed until light and fluffy, approximately 5 minutes. Scrape down the sides of the bowl and mix on high speed for another 30 seconds. Turn the mixer speed down to medium low and add the eggs and yolks, one at a time, allowing them to incorporate completely before adding the next. Scrape down the sides of the bowl, add the vanilla and brandy and then mix again until everything is just combined.
On low speed, add the dry ingredients in 3 batches and mix until the batter is just combined.
Peel and core the apple, then slice it in half from top to bottom. With the flat sides down, slice each apple thinly.
Spread a small amount of the batter into the reserved loaf pan. Layer the apples in the pan, overlapping each other, until the bottom of the pan is covered. Pour in the rest of the batter and smooth the top with a spatula.
Bake the poundcake for 70-75 minutes, or until a toothpick inserted into the center comes out clean. Allow the cake to cool for 5 minutes in the pan and then gently flip onto a cooling rack. Allow the cake to cool to room temperature.
While the cake is cooling, prepare the caramel sauce. Add the sugar and water to a medium saucepan and bring to a boil. Reduce the heat slightly and simmer until the caramel reaches a dark amber color. Do not walk away; caramel can go from perfect to burnt in a matter of seconds. Add the cream and quickly pull your hand away because the mixture will splatter. After a moment it will calm down. Stir with a heat proof spatula or whisk until the sauce is smooth. The sugar may seize up at first which is fine; just keep stirring over the heat. Add the salt and allow the sauce to reduce, while stirring, until it reaches the desired thickness (5-10 minutes).
Before serving, drizzle the caramel sauce over the cake.