Preheat the Oven: Preheat your oven to 350°F (175°C). Grease and flour two 9-inch cake pans.
Prepare the Dry Ingredients: In a large bowl, whisk together flour, sugar, cocoa powder, baking soda, baking powder, and salt.
Mix Wet Ingredients: In a separate bowl, beat together eggs, vanilla extract, brewed espresso, milk, and vegetable oil.
Combine: Gradually add the wet ingredients to the dry ingredients and mix until smooth.
Bake: Divide the batter between the cake pans. Bake for 25-30 minutes or until a toothpick comes out clean.
Make the Caramel Sauce: In a saucepan, melt sugar over medium heat until golden. Stir in butter and heavy cream. Cook for another 2-3 minutes. Remove from heat and stir in vanilla and salt. Let cool.
Prepare the Coffee Buttercream: Beat softened butter until fluffy. Gradually add powdered sugar, followed by brewed espresso and vanilla. Continue beating until smooth and creamy.
Assemble the Cake: Once the cake layers have cooled, spread coffee buttercream between the layers. Drizzle caramel sauce on top and serve.