Step 1: Prepare the Oven and Baking Pan

• Preheat your oven to 350°F (175°C). Grease a 9×5-inch loaf pan with butter and dust it with flour, or line it with parchment paper for easy removal.

Step 2: Mix the Dry Ingredients

• In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.

Step 3: Cream the Butter and Sugar

• In a large bowl, beat the butter and sugar using an electric mixer on medium speed until the mixture is light and fluffy (about 3-4 minutes). This step is crucial for creating a light texture in the cake.

Step 4: Add the Eggs and Vanilla

• Add the eggs, one at a time, beating well after each addition. Scrape down the sides of the bowl as needed. Stir in the vanilla extract.

Step 5: Incorporate the Dry Ingredients and Milk

• Gradually add the dry ingredients to the butter mixture, alternating with the milk, beginning and ending with the flour mixture. Mix just until combined—do not overmix.

Step 6: Prepare the Chocolate Batter

• In a small bowl, combine the cocoa powder and hot water to form a smooth paste. Take about 1 cup of the vanilla batter and fold it into the cocoa paste to create the chocolate batter.

Step 7: Create the Marble Effect

• Pour half of the vanilla batter into the prepared loaf pan. Drop spoonfuls of the chocolate batter on top, followed by the remaining vanilla batter. Use a knife or skewer to gently swirl the batters together, creating a marbled effect.

Step 8: Bake the Cake

• Bake the cake in the preheated oven for 50-60 minutes, or until a toothpick inserted into the center comes out clean. Let the cake cool in the pan for 10 minutes before transferring it to a wire rack to cool completely.

Step 9: Make the Espresso Glaze

• In a small bowl, whisk together the powdered sugar, brewed espresso, vanilla extract, and a pinch of salt until smooth. If the glaze is too thick, add a bit more espresso; if it’s too thin, add more powdered sugar.

Step 10: Glaze the Cake

• Once the cake has cooled, drizzle the espresso glaze over the top, letting it drip down the sides for a beautiful finish.