Preheat the oven to 350°F (175°C). Grease and line two 9-inch round cake pans with parchment paper.

In a large mixing bowl, whisk together the flour, sugar, cocoa powder, baking powder, baking soda, and salt.

In another bowl, mix the buttermilk, vegetable oil, eggs, and vanilla extract until well combined.

Gradually add the wet ingredients to the dry ingredients, mixing until just combined.

Stir in the hot espresso until the batter is smooth.

Divide the batter evenly between the prepared cake pans.

Bake for 25 minutes or until a toothpick inserted in the center comes out clean.

Let the cakes cool in the pans for 10 minutes, then remove from pans and cool completely on a wire rack.

In a saucepan, melt the butter over medium heat, stirring constantly until it turns golden brown and has a nutty aroma.

Remove from heat and let it cool slightly.

In a mixing bowl, combine the browned butter, powdered sugar, heavy cream, and vanilla extract. Beat until smooth and creamy.

Place one cake layer on a serving plate. Spread a layer of frosting on top.

Top with the second cake layer and frost the top and sides of the cake.

Decorate as desired and serve.