In a medium saucepan, combine granulated sugar and water over medium heat. Stir gently to dissolve the sugar, then allow it to boil without stirring until the mixture turns a beautiful amber color, about 8-10 minutes. Once done, carefully whisk in butter and heavy cream until smooth. Set aside to cool completely.

Preheat your oven to 350°F (175°C). Grease and flour two 6-inch round cake pans. In a large mixing bowl, whisk together all-purpose flour, cocoa powder, baking powder, baking soda, and salt. In another bowl, mix room-temperature butter, granulated sugar, brown sugar, eggs, Greek yogurt, buttermilk, and vanilla until smooth. Combine the dry and wet mixtures, then gently fold in the hot espresso.

Evenly distribute the rich batter between your prepared cake pans, smoothing the tops. Bake for about 25 minutes or until a toothpick inserted comes out clean. Allow to cool in the pans for 10 minutes before transferring to a wire rack.

In a large mixing bowl, beat the room temperature butter until light and fluffy, about 3-5 minutes. Gradually mix in the espresso powder and vanilla extract, then carefully add powdered sugar a cup at a time. Finally, blend in cooled espresso until buttercream reaches a light and fluffy consistency.

Once the cakes are completely cool, place one layer on a serving plate. Spread a layer of buttercream atop the first layer, followed by a drizzle of salted caramel. Carefully position the second layer on top and frost the top and sides with the remaining buttercream.

Once assembled, slice and serve your Salted Caramel Espresso Chocolate Cake! Enjoy with whipped cream or vanilla ice cream for an extra touch.