Combine 1 cup sugar and 1/4 cup water in a saucepan over medium heat. Stir until sugar dissolves. Increase heat and boil, without stirring, until it turns a deep amber color. Remove from heat and slowly whisk in 1/2 cup warmed heavy cream, then stir in 4 tbsp butter and 1 tsp sea salt until smooth. Set aside to cool completely.

Preheat oven to 350°F (175°C). Grease and flour two 8-inch round cake pans. In a large bowl, cream 1 cup softened butter and 1.5 cups sugar. Beat in 3 eggs and 1 tsp vanilla. In a separate bowl, whisk 2.5 cups flour, 1.5 tsp baking powder, 0.5 tsp baking soda, and 0.5 tsp salt. Alternate adding dry ingredients and a mixture of 1 cup buttermilk and 0.5 cup coffee to the butter mixture, ending with dry ingredients. Mix until just combined.

Divide batter evenly between the pans. Bake for 30-35 minutes, or until a toothpick comes out clean. Let cool in pans for 10 minutes before inverting onto a wire rack to cool completely.

Beat 1.5 cups softened butter until creamy. Gradually add 4 cups sifted powdered sugar. Add dissolved espresso powder, 1 tsp vanilla, and a pinch of salt. Beat until combined. Add 2-3 tbsp heavy cream until it reaches a spreadable consistency.

Place one cake layer on a plate. Top with a layer of buttercream and a drizzle of caramel. Add the second cake layer. Frost the top and sides with the remaining buttercream. Drizzle with remaining caramel sauce. Refrigerate for 30 minutes before serving.