Preheat your oven to 350°F (175°C). Grease and flour two 8-inch round cake pans, then line the bottoms with parchment paper and set aside. In a medium mixing bowl, cream together the butter and sugar until light and fluffy. Beat in the eggs one at a time, then continue mixing on high speed for about 3 minutes, until the mixture becomes pale and airy. Stir in the vanilla extract or paste. In a separate bowl, whisk together the flour, baking powder, and salt. Add the dry ingredients to the creamed mixture in three additions, alternating with the milk and beginning and ending with the dry mixture. Mix until just combined, being careful not to overbeat. Evenly divide the batter between the prepared pans and smooth the tops with the back of a spoon or spatula. Bake for 30 to 40 minutes, or until a toothpick inserted into the center comes out clean. Let the cakes cool in the pans for 5–10 minutes, then turn them out onto a wire rack to cool completely.

For the frosting, beat the softened butter until smooth and fluffy. Gradually add the powdered sugar, one cup at a time, and mix until fully incorporated. Add ⅓ cup of the cooled caramel sauce and beat again until light and fluffy. If the frosting appears too thick, add 1 to 2 tablespoons of cream or milk to adjust the consistency.

To assemble the cake, place one cake layer on a serving plate or cake stand. Use a fork to gently poke holes across the surface of the cake. Carefully pour about ⅓ cup of the caramel sauce over the top, allowing it to seep into the holes. Spread a thick layer of frosting over the caramel-soaked layer. Add the second cake layer on top, with the flattest side facing up. Repeat the process of poking holes, drizzling with the remaining caramel sauce, and spreading on the frosting. For an extra touch, sprinkle flaky sea salt over the top if desired.