Baking spray that contains flour may be used to grease and flour the pans. Both natural and Dutch-processed cocoa will work in this recipe. When taking the temperature in steps 3 and 4, remove the pot from the heat and tilt the pan to one side. Use your thermometer to stir the caramel back and forth to equalize hot and cool spots and make sure that you are getting an accurate temperature.
1. For the cake: Adjust oven rack to middle position and heat oven to 325º F. Grease two 9-inch round cake pans, line with parchment paper, grease parchment paper, and flour pans. Sift flour and cocoa into large bowl. Whisk in sugar, baking soda, baking powder and salt. Whisk buttermilk, water, oil, eggs and vanilla together in second bowl. Whisk buttermilk mixture into flour mixture, until smooth batter forms. Divide batter evenly between prepared pans and smooth tops with spatula (weight the pans on a kitchen scale to ensure that batter is divided evenly).
2. Bake until toothpick inserted in center comes out clean, 22 to 28 minutes, switching and rotating pans halfway through baking. Let cakes cool in pans on wire rack for 15 minutes. Remove cakes from pans, discarding parchment, and let cool completely on rack, at least 2 hours.
3. For the caramel filling: Lightly grease 8-inch square baking pan. Combine sugar, corn syrup and water in medium saucepan. Bring to boil over medium-high heat and cook, without stirring, until mixture is amber-colored, 8 to 10 minutes. Reduce heat to low and continue to cook, swirling saucepan occasionally, 20 5 minutes longer (caramel will register between 375 and 380 degrees F.).
4. Off heat, carefully stir in cream, butter, vanilla and salt (mixture will bubble and steam). Return saucepan to medium heat and cook, stirring frequently, until smooth and caramel reaches 240 to 245 degrees F., 3 to 5 minutes. Carefully transfer caramel to prepared pan and let cool, until just warm (100 to 105 degrees F.), 20 to 30 minutes.
5. For the frosting: Process butter, sugar, cocoa and salt in food processor, until smooth, about 30 seconds, scraping down the sides of bowl, as needed. Add corn syrup and vanilla and process until just combined, about 5 to 10 seconds. (Frosting may be made up to 3 hours in advance. For longer storage, cover and refrigerate frosting. Let stand at room temperature for 1 hour, before using).
6. Using long serrated knife, score 1 horizontal line around sides of each cake layer, then, following scored lines, cut each layer into 2 even layers.
7. Using rubber spatula or large spoon, transfer 1/3 of the caramel sauce to center of 1 cake layer and use small offset spatula to spread surface, leaving 1/2 inch border around the edge. Repeat with remaining caramel and 2 of remaining cake layers. (Three of your cake layers should be topped with caramel).
8. Line edges of cake platter with 4 strips of parchment to keep platter clean. Place 1 caramel-covered cake layer on platter. Top with second caramel-covered layer. Repeat with third caramel-covered layer, and top with final layer. Spread frosting evenly over sides and top of cake. Let cake stand for at least 1 hour. (Cake may be made up to 2 days in advance and refrigerated. Let stand at room temperature for at least 5 hours, before serving). Sprinkle with coarse sea salt. Cut and serve.