Preheat oven and prep cake pans: Preheat oven to 350 degrees. Butter three 9-inch round cake pans, and dust with flour, tapping out excess.

Sift dry ingredients for cake and mix: Sift flour, granulated sugar, cocoa, baking soda, baking powder, and 1 ½ teaspoons coarse salt into the bowl of a mixer. Beat on low speed until just combined.

Add eggs, buttermilk, warm water, oil, and vanilla: Raise speed to medium, and add eggs, buttermilk, 1 ½ cups warm water, oil, and vanilla. Beat until smooth, about 3 minutes.

Transfer batter to prepared pans and bake: Divide batter among pans. Bake until cakes are set and a toothpick inserted into the center of each comes out clean, about 35 minutes.

Cool cakes: Let cool in pans set on a wire rack for 15 minutes. Turn out cakes onto racks, and let cool completely.

Make the caramel: Combine granulated sugar, corn syrup, and ¼ cup water in a medium saucepan over high heat. Cook, without stirring, until mixture is dark amber, about 14 minutes.

Add cream and cook: Remove from heat, and carefully pour in cream (mixture will spatter); stir until smooth. Return to heat, and cook until a candy thermometer reaches 238 degrees, about 2 minutes.

Transfer caramel to bowl, add salt, then butter, and cool: Pour caramel into a medium bowl, stir in 1 teaspoon coarse salt, and let cool slightly, about 15 minutes. Stir in butter, 1 tablespoon at a time. Let cool completely.

Whisk cocoa and water for frosting: While caramel is cooling, whisk together cocoa and ¼ cup plus 2 tablespoons warm water in a bowl until cocoa dissolves.

Beat butter, confectioner' sugar, and salt; add melted chocolate gradually: Beat butter, confectioners' sugar, and a generous pinch of coarse salt in a clean bowl with a mixer on medium speed until pale and fluffy. Gradually beat in melted chocolate and then cocoa mixture until combined. Let stand for 30 minutes before using.

Trim and halve cakes horizontally: Trim tops of cakes using a serrated knife to create a level surface. Cut each in half horizontally to form 2 layers.

Assemble cake: Transfer 1 layer to a serving platter, and spread ¾ cup caramel over top. Top with another cake layer, and repeat with remaining caramel and cake layers, leaving top uncovered. Refrigerate until set, about 1 hour.

Frost cake: Frost top and sides of cake in a swirling motion. Sprinkle with sea salt.