Preheat oven to 350℉. Liberally grease 3, 9-inch cake pans and line the bottoms with parchment paper circles.
In a medium bowl sift together the flour, salt, baking soda and baking powder. Set aside.
In a large mixing bowl using an electric mixer, cream together the butter and sugar until light and fluffy, about 3-4 minutes.
Add the vanilla extract and the eggs one at a time, until fully incorporated and scraping the bowl after each egg addition. Add in ⅓ of the buttermilk, followed by ⅓ of the flour mixture. Stir after each addition, then continue alternating buttermilk and flour until just combined.
Evenly divide the batter into the prepared cake pans and smooth out the batter.
Bake 20-25 minutes until a toothpick inserted in the center comes out clean and the center springs back when lightly touched.
Cool in the pans for 10 minutes, then remove from the pans to a cooling rack and cool completely.
Salted Caramel
Fill a small glass with hot water, and have a silicone pastry brush ready.
In a large sauce pot, dissolve sugar completely in hot water over medium low, whisking until dissolved and mixture is completely clear, do not allow to boil until sugar is fully dissolved.
Once sugar is dissolved, stop whisking and increase heat to medium. Swirl the pan, do not stir or whisk, until the sugar is a rich amber color. If sugar crystals form on the side of the pan, dip the pastry brush in hot water and wash the crystals down into the caramel. If crystals touch the boiling sugar, it will cause your caramel to seize up.
Once the sugar is a rich amber color, remove from heat and whisk in the cubed butter carefully, it will foam up rapidly, but keep whisking until fully combined.
Whisk in the heavy cream, followed by the vanilla, and return to the heat for 1 minute, whisking rapidly. Remove from heat and pour into a glass bowl or jar to cool to room temperature.
You can also split the recipe in half, making two small batches if desired. Two small batches should be made for safety reasons if you do not have a large pot suitable for making caramel.
Buttercream
In the bowl of a stand mixer, using a paddle attachment, cream together the butter and 1 cup of the cooled caramel sauce until smooth and combined, about 2-3 minutes.
Add the vanilla and salt and mix until combined. Scrape the sides and bottom to be sure everything is evenly incorporated.
With the mixer on a medium low speed slowly add 5 ½ cups of powdered sugar, scraping occasionally. If the frosting is too thick, add in a tablespoon or two of milk to thin it out to a good piping consistency. If it is too thin, add a bit more powdered sugar. Whip this mixture for 2-3 minutes until it is light and fluffy.
Assembly
If desired, once cakes have completely cooled, level off the tops of the cakes with a large serrated knife. Fill a large piping bag fitted with a ½” round tip with buttercream.
On a cake stand or large platter place the first cake layer bottom side up. Spoon on ¼ cup of the remaining caramel sauce and smooth this thin layer evenly on top of the cake, leaving a ½” border around the outside so that the caramel doesn't ooze out when you smooth the buttercream. Follow this by piping a ring of buttercream all the way to the edge of the cake and smooth it gently with an offset spatula.
Place the next cake layer on top and gently press into the bottom layer, repeat the same process with the caramel and buttercream.
Place the final cake layer on top and very gently press down into the bottom 2 layers. Frost the sides and top of the cake with the remaining buttercream.
For garnish, top the cake with more caramel sauce, allowing some to drip down the edge of the cake and finish with a sprinkle of a flakey sea salt.
Notes
When making the caramel sauce, it is important to use a large size sauce pan. The caramel mixture will bubble up violently when you add in the butter and cream and if your pan is too small it will boil over and cause a huge mess and potentially burn your skin. If caramel sauce does get on your skin, resist the urge to wipe it off and instead submerge into ice cold water.