Preheat the oven to 350°F. Grease a 13-by-9-by-2-inch baking pan.

Whisk together the cake flour, baking soda and salt in a medium bowl. Set aside.

In a measuring cup or small bowl, combine the vinegar, milk and vanilla extract. The mixture may look slightly curdled; this is normal.

In a large mixing bowl, beat the eggs, brown sugar and melted chocolate together for 1 minute.

Add the flour mixture, softened butter and half of the milk mixture. Mix just until the flour is moistened.

Beat for 1 minute, scraping down the sides and bottom of the bowl as needed.

Add the remaining milk mixture and mix just until combined.

Spread the batter evenly in the prepared pan. Bake for 30–35 minutes, or until a toothpick inserted in the center comes out clean or with a few moist crumbs.

Let the cake cool completely in the pan before frosting.

Place the semi-sweet chocolate in a microwave-safe bowl. Microwave in 20-second intervals, stirring after each interval, until melted and smooth. Let the chocolate cool slightly.

Gradually stir the sour cream into the melted chocolate until the frosting is completely smooth and creamy.

Spread the frosting evenly over the cooled cake. Slice and serve.