Preheat the oven to 325°F. Grease a 9x5-inch loaf pan and dust with flour.
In a mixing bowl, whisk together the flour, baking powder, and salt. Set aside.
Separately, in a large bowl, beat the softened butter and sugar with an electric mixer until light and fluffy, about 2 minutes.
Incorporate the eggs into the butter mixture individually, ensuring to beat thoroughly after each addition. Stir in the vanilla extract.
Gradually add the dry ingredients to the wet mixture, alternating with the milk. Begin and end with the dry ingredients. Mix until just combined.
Split the batter evenly between two bowls. In a separate small bowl, combine cocoa powder with hot water to create a smooth paste. Incorporate this mixture into one bowl of batter, stirring until thoroughly blended.
Spoon vanilla and chocolate batters alternately into the pan. Use a knife to swirl them for a marbled effect. Bake for 60-70 minutes or until a toothpick comes out clean. Cover the cake for the last 20 minutes to prevent overbrowning if needed.
Allow the cake to cool in the pan for 10 minutes, then remove it to a wire rack to cool completely before slicing.