Instructions

for the cake

Adjust oven rack to middle position and heat oven to 325 degrees. Grease two 9-inch round cake pans, line with parchment paper, grease parchment, 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 rubber spatula.
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.

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, until dark amber, 2 to 5 minutes longer. (Caramel will register between 375 and 380 degrees.)
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, 3 to 5 minutes. Carefully transfer caramel to prepared pan and let cool until just warm to touch (100 to 105 degrees), 20 to 30 minutes.

for the frosting

Process butter, sugar, cocoa, and salt in food processor until smooth, about 30 seconds, scraping down sides of bowl as needed. Add corn syrup and vanilla and process until just combined, 5 to 10 seconds. Scrape down sides of bowl, then add chocolate and pulse until smooth and creamy, 10 to 15 seconds. (Frosting can be made 3 hours in advance. For longer storage, cover and refrigerate frosting. Let stand at room temperature for 1 hour before using.)
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.
Using rubber spatula or large spoon, transfer 1/3 of caramel to center of 1 cake layer and use small offset spatula to spread over surface, leaving 1/2-inch border around edge. Repeat with remaining caramel and 2 of remaining cake layers. (Three of your cake layers should be topped with caramel.)
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. Carefully remove parchment strips. Let cake stand for at least 1 hour. (Cake can be made 2 days in advance and refrigerated. Let stand at room temperature for at least 5 hours before serving.) Sprinkle with coarse sea salt, if using. Cut and serve.