For the cake:
4 ounces unsweetened chocolate
1/2 cup butter (1 stick), plus 1 tablespoon for greasing the pan
2 cups sifted flour
2 cups granulated sugar
1/4 teaspoon salt
1 cup sour cream
1 teaspoon vanilla extract
1 1/2 teaspoons baking soda
2 eggs, beaten
For the frosting:
4 ounces unsweetened chocolate
7 tablespoons whole milk
3 cups powdered sugar
1 pinch salt
1 teaspoon rum extract (you can also use vanilla extract)
1/3 stick of butter, melted
For the cake:
Preheat the oven to 350°F and grease a 13- x 9- x 2-inch pan with 1 tablespoon of butter.
Melt the chocolate over a double boiler.
In a separate saucepan, melt the 1/2 cup butter over medium heat along with 1 cup of hot water and bring to a low boil. Mix in the melted chocolate and stir to combine. Take off the heat.
In a medium-size bowl, combine the sifted flour, sugar, and salt.
Pour the chocolate mixture into the bowl with the flour mixture and combine well with a wooden spoon. Add the sour cream, vanilla, and baking soda to the mixture and combine well. Add the beaten eggs and mix until they're fully incorporated.
Add the batter to the greased cake pan and bake for 30 minutes, or until you can insert a toothpick or knife into the center and it comes out clean. Let cool completely before frosting.
For the frosting:
Melt the chocolate in a double boiler.
In a medium-size bowl, mix the milk and sugar gradually.
Add the salt and rum extract to the milk-sugar mixture and stir until combined. Then add the melted chocolate and stir until combined.
Add the melted butter and mix until fully incorporated.
Let the frosting cool slightly, before spreading on cooled cake.