Preheat the oven to 350°F (175°C). Grease a 9-inch round cake pan or line it with parchment paper.
Mix the wet ingredients: In a large bowl, cream together the softened butter and sugar. Add eggs one at a time, mixing well after each addition. Stir in the milk and vanilla extract.
Prepare the dry ingredients: In another bowl, sift together the flour, cocoa powder, and baking powder.
Combine wet and dry ingredients: Gradually add the dry mixture to the wet ingredients, mixing until just combined. Be careful not to overmix.
Add the melted chocolate: Fold in the melted dark chocolate until the batter is smooth and evenly combined.
Bake: Pour the batter into the prepared cake pan and spread it evenly. Bake for 30-35 minutes or until a toothpick inserted into the center comes out clean.
Cool: Let the cake cool in the pan for 10 minutes, then transfer it to a cooling rack to cool completely before frosting.
