Preheat the oven to 350° F (180º F). Lightly grease a 9.5 x 5-inch loaf pan. In a large bowl combine the flour, baking powder, baking soda, and salt. Reserve.
In a mixing bowl, combine milk and vinegar. Let the mixture stand at room temperature for 5 minutes. When it is ready, the milk will be slightly thickened, and you will see small curdled bits. Reserve.
In a large bowl, beat butter and sugar until creamy on medium-high speed, for 3 - 4 minutes. Scrape down the sides and up the bottom of the bowl with a rubber spatula as needed. Add vanilla; continue beating to combine.
Reduce speed to low and add half of the flour mixture. Scrape down the mixing bowl with a spatula and turn the batter over several times to ensure all of the ingredients are well incorporated. Add milk mixture; continue beating to incorporate. Add the remaining flour; beat just until combined. Do not overmix this batter. The batter will be slightly thick, and that is okay.
Stir together hot water, cocoa and instant coffee powder (if using) until smooth and well combined.
Take one-third of the vanilla batter and place it in a small bowl. Fold the cocoa mixture into the batter until blended.
Spread a cup of vanilla batter in the bottom of the pan. Dollop on half of the chocolate batter, then repeat with another heaping cup of vanilla batter, the remainder of the chocolate, and top with the rest of the vanilla batter. NOTE: There's no need to swirl the batters together to get a marbled effect.
Bake the cake for 40 to 50 minutes, or until a skewer comes out clean when poked in the center. Baking times vary, so keep an eye on yours. Test it with a cake tester; if it's not quite done, give it another 5 minutes. The cake is done when a toothpick inserted in the center comes out clean. If you find the top of the cake is browning too quickly in the oven, loosely cover it with aluminum foil after 40 min of baking.
Remove the cake from the oven, and after 10 minutes turn it out of the pan onto a rack to cool.