In a medium heavy-bottomed saucepan, spread sugar in an even layer and cook over medium heat without stirring. Let it melt and turn amber, swirling the pan occasionally, about 8-10 minutes until it reaches a deep copper color.

Remove from heat and immediately whisk in butter until melted and smooth. Carefully pour in warm cream (it will bubble vigorously) and whisk until silky. Stir in salt. Pour into a heatproof bowl and let cool completely, about 45 minutes. You'll use about half for the cake; save the rest for drizzling.

Preheat oven to 350 degrees F. Butter and flour two 9-inch round pans, or line with parchment. In a large bowl, whisk together flour, cocoa powder, sugar, baking soda, and salt until no lumps remain.

Add buttermilk, oil, eggs, and vanilla. Beat with an electric mixer on medium speed for 2 minutes until smooth. The batter will be thick. With mixer on low, slowly pour in coffee and mix just until combined. The batter will thin out considerably.

Divide evenly between pans. Bake 30-35 minutes until a toothpick comes out with a few moist crumbs. Cool in pans 15 minutes, then turn out onto racks to cool completely.

Beat softened butter until creamy, about 2 minutes. Add cocoa and beat until combined. Gradually add powdered sugar on low speed, then pour in cream, vanilla, and salt. Beat on medium-high for 3 minutes until light and fluffy. Add more cream by the tablespoon if needed for spreading consistency.

Place one cake layer on a plate. Spread 1/2 cup of cooled caramel over top, leaving a 1/2-inch border. Top with second layer. Frost the entire cake with chocolate frosting. Drizzle reserved caramel over the top, letting it drip down the sides. Chill 20 minutes to set before slicing.