Preheat the oven to 350 degrees F. Grease a 9x13-inch baking dish and set aside. Mix the flour, baking powder, baking soda, salt, cinnamon and nutmeg in a bowl.
In the bowl of an electric mixer, cream the butter and sugar together until light and fluffy, 3-5 minutes. Scrape the bowl and slowly beat in the eggs and vanilla. Alternate add the flour mixture and milk until the batter is smooth. Then scrape the bowl again and stir in the apple by hand.
Scoop the batter into the prepared baking dish. Smooth out the top and bake for 40-50 minutes until a toothpick inserted into the center of the cake comes out clean. Cool to room temperature.
For the Salted Caramel Frosting:
While the cake is baking, place the brown sugar and water in a large deep skillet. (You want to have a large heating surface.) Turn on medium heat and bring to a simmer. Stir and allow the liquid to bubbly for approximately 5 minutes, until the sugar syrup is very dark. Remove the pan from the burner and whisk in the heavy cream, vanilla, and salt. Place the pan in the refrigerator to cool to room temperature. (If you add it to the butter while it's warm, it will melt the butter and ruin the frosting.)
Once the caramel has cooled to room temperature, place the butter in the bowl of an electric mixer and beat until smooth. Then add in the caramel. Beat again to combine. Then scrape the bowl and slowly add the powdered sugar. Beat until smooth.
Scoop the frosting on top of the completely cooled cake and spread over the top. Cut into 24 pieces and enjoy!