Preheat your oven to 350°F (175°C). Grease and flour three 9-inch round cake pans.

In a heatproof bowl, melt the chopped dark chocolate over a pot of simmering water or in the microwave, stirring occasionally until smooth. Set aside to cool slightly.

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

In another bowl, whisk together the eggs, milk, oil, and vanilla extract. Stir in the melted chocolate until well combined.

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

Slowly pour in the hot coffee, stirring until the batter is smooth and well incorporated.

Divide the batter evenly among the prepared cake pans.

Bake in the preheated oven for 25-30 minutes, or until a toothpick inserted into the center of the cakes comes out clean.

Remove the cakes from the oven and let them cool in the pans for 10 minutes. Then, transfer them to wire racks to cool completely.

In a large mixing bowl, beat the softened butter until creamy and smooth.

Gradually add the powdered sugar, melted chocolate, salt, and vanilla extract, alternating with the heavy cream or milk. Beat on low speed until combined.

Increase the speed to medium-high and beat until the frosting is light and fluffy, scraping down the sides of the bowl as needed.