For the marble cake: Preheat oven to 350° F. Very lightly spray bottom and sides of a 15" x 10" x 1" rimmed pan with cooking spray. This is the pan I use. Set aside.

In a small cup or bowl, gently melt the semisweet chocolate. Take care to not let it scorch. Set aside to cool to room temperature.

In small bowl, whisk together flour, baking powder, and salt. Set aside.

In large bowl, beat butter and sugar with electric mixer on medium speed for 2 minutes, scraping bowl occasionally, until fluffy. Beat in eggs, one at a time, just until smooth. Beat in vanilla. On low speed, beat in one-third of the flour mixture, then the whole milk, beating after each addition, just until smooth. Repeat with flour mixture and then ½ cup of the sour cream, ending with flour mixture, scraping side of bowl occasionally. Spread 3½ cups of vanilla batter evenly into pan.

In a small cup or bowl, whisk together cocoa powder and baking soda. Add to remaining vanilla batter along with remaining 1 tablespoon of sour cream and cooled melted semisweet chocolate. Fold until thoroughly combined into a chocolate batter. Spoon chocolate batter by generous tablespoonfuls evenly onto vanilla batter. Cut through mixture several times with a butter knife for marbled design. Firmly tap pan on counter several times to eliminate air bubbles and settle the batter evenly into the pan.

Bake 20 to 22 minutes, or until toothpick inserted in center comes out clean. Set on baking rack to cool completely.

For the double chocolate buttercream: In a medium microwave-safe bowl, gently microwave chocolate chips uncovered until they are about halfway melted. Take care to not scorch the chocolate. Remove from microwave and stir until smooth. Let cool for 5 to 10 minutes, until just barely warm.

In a small bowl, whisk together powdered sugar, baking cocoa, and kosher salt. Add butter to melted and cooled chocolate, along with powdered sugar mixture, half & half, and vanilla. Beat with electric mixer on medium speed until smooth and creamy, scraping side of bowl occasionally. Spread on top of cooled cake. Cut cake into pieces and serve.