Preheat oven to 325 degrees. Lightly brush a 9-by-5-inch loaf pan with butter; dust with cocoa powder, tapping out excess. In a medium bowl, whisk together flour, cocoa powder, baking soda, and salt; set aside.

With an electric mixer on high speed, beat butter and granulated sugar until pale and fluffy, about 4 minutes. Scrape down sides of bowl. Reduce speed to medium; add eggs, one at a time, beating thoroughly after each addition and scraping down bowl as needed. Beat in 1/2 teaspoon vanilla and vinegar. Reduce speed to low; add flour mixture in 3 batches, alternating with buttermilk and starting and ending with flour mixture, until just combined. Add food coloring; beat until fully incorporated.

Pour batter into prepared pan. Tap pan on counter; smooth top with an offset spatula. Bake until a tester inserted in center comes out clean, about 1 hour 20 minutes, tenting with foil if browning too quickly. Transfer pan to a wire rack and let cool 15 minutes, then turn cake out of pan onto rack and let cool completely. Cake can be stored, wrapped in plastic, at room temperature up to 2 days.

When ready to serve, beat cream cheese with confectioners' sugar and remaining 1/4 teaspoon vanilla extract until smooth. Spread with a spatula over top of cake. Slice and serve.