Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking pan with butter or non-stick spray, then line with parchment paper, leaving an overhang on the sides for easy removal later.
In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
In a large bowl using an electric mixer, beat the softened butter and granulated sugar on medium-high speed until light and fluffy, about 3-4 minutes.
Add eggs one at a time, beating well after each addition. Stir in the vanilla extract.
Gradually add the flour mixture to the butter mixture, alternating with buttermilk, beginning and ending with flour (three additions of flour, two of buttermilk). Mix just until combined after each addition.
Gently fold in the diced apples until evenly distributed throughout the batter.
Spread the batter evenly in the prepared baking pan. Bake for 35-40 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs.
While the cake is baking, make the caramel sauce. In a medium saucepan over medium heat, combine the brown sugar and butter. Bring to a gentle boil, stirring constantly for 2 minutes until sugar dissolves completely.
Remove from heat and carefully stir in the heavy cream, vanilla, and half of the sea salt. The mixture will bubble vigorously—this is normal! Let cool slightly until the cake is ready.
When the cake is done, remove from oven and let cool in the pan for 10 minutes. Poke holes all over the warm cake using a wooden skewer or fork.
Pour about ¾ of the warm caramel sauce over the cake, ensuring it seeps into the holes. Sprinkle with remaining sea salt while the caramel is still warm.
Allow the cake to cool completely before cutting into squares. Just before serving, warm the reserved caramel sauce slightly and drizzle over individual portions.