For the yellow cake:

1. Preheat oven to 350°F with a rack in the center. Butter and flour a 9 x 13-inch baking pan, tapping out any excess flour.
2. Into a medium bowl, sift together the cake flour, baking powder, and salt.
3. In a large bowl or stand mixer fitted with the whisk attachment, beat the butter and sugar together on medium-high until pale and fluffy, about 5 minutes. Beat in the eggs one at a time. Add the vanilla and beat for 5 minutes more.
4. Reduce speed to low and alternate adding the flour mixture (in 3 parts) and the milk (in 2 parts), starting and ending with flour. Mix just until smooth — do not overmix.
5. Spread the batter into the pan and bake about 20 minutes (check at 18 minutes), until a cake tester comes out clean from the center. The cake will be pale, not brown. Cool completely before frosting.

For the chocolate frosting:

1. Melt the chopped chocolate in a heatproof bowl set over a saucepan of barely simmering water, stirring occasionally, until smooth. Remove from heat and let cool to room temperature (the chocolate should be fluid but not hot — about 90°F / 32°C).
2. Stir the sour cream and butter into the cooled chocolate until fully incorporated.
3. Sift in the powdered sugar and a pinch of salt. Stir until smooth and glossy. If the frosting is too soft, refrigerate for 10–15 minutes until it reaches a spreadable consistency.
4. Spread evenly over the completely cooled cake.