Preheat the oven to 350°F (175°C). Grease and flour a 9-inch round cake pan or line it with parchment paper.
In a medium bowl, whisk together the flour, sugar, cocoa powder, baking soda, baking powder, and salt.
In another bowl, whisk the egg, sourdough starter, milk, oil, and vanilla extract until fully combined. Gradually mix in the dry ingredients until smooth.
Carefully pour in the boiling water, stirring gently to combine. This will create a thin batter, which is expected.
Pour the batter into the prepared cake pan and bake for 35-40 minutes, or until a toothpick inserted comes out clean. Let it cool completely on a wire rack.
In a large bowl, beat the softened butter with an electric mixer until creamy. Gradually add powdered sugar, cocoa powder, vanilla extract, and salt. Mix until smooth. Add heavy cream, a little at a time, until you achieve the desired consistency.
Once the cake is cool, frost with the chocolate buttercream frosting. Spread evenly with a spatula.
Serve and enjoy! Let the cake sit for a few minutes to allow the frosting to set before slicing.