Preheat the oven to 350°F. Place the oven rack in the bottom third of the oven. Generously grease a Bundt pan or large round cake pan with butter.
In a large mixing bowl with an electric hand whisk, or in a stand mixer with a paddle attachment, beat the softened butter, granulated sugar, and salt together on a medium speed, until it’s pale, smooth, and creamy after 2 to 3 minutes.
Scrape down the sides of the bowl with a silicone spatula. Add the vanilla and mix for about 30 seconds.
Add one egg at a time, beating for about 30 seconds after each addition. Beat until each egg is mixed in, and scrape the sides of the bowl with a rubber spatula, before adding the next egg. (It’s okay if it looks split or curdled at this step. It’ll come together once everything else is mixed in.)
Add the milk and beat again for 30 seconds. Set aside.
In a separate large mixing bowl, whisk together the flour and baking powder.
Gradually add the flour mixture to the egg mixture while mixing on a low speed. Scrape the sides of the bowl so there are no pockets of dry flour. (The batter will look pretty thick at this point, which is normal.)
Pour two-thirds of the cake batter into the prepared baking pan.
To make the chocolate cake, add the cocoa powder, espresso powder, and milk to the remaining one-third cake batter in the mixing bowl. Mix until it’s fully combined, scraping the sides of the bowl.
Pour the chocolate cake batter on top of the light-colored cake batter, and drag the blade of a knife through the mixture to swirl the two colors together. This will create the marbled effect with the two colored cake batters. Be careful not to swirl the batter too much, or you’ll lose the contrast between the light and dark batters.
Bake for 45 to 60 minutes, until a toothpick or knife inserted into the center of the cake comes out clean.
Let the cake cool on a cooling rack for 10 minutes. Then turn the cake upside down to release it from the Bundt pan. Let the cake continue to cool completely on the cooling rack. Dust the cake with powdered sugar and enjoy!!