Preheat oven to 350°F (177°C) and prepare an 8.5x4.5 inch loaf pan by greasing and lining it with parchment paper, or grease and flour the pan.

Gently melt the butter in a small pan, then remove from heat and stir until fully melted to ensure it cools adequately before mixing with eggs.

In a large mixing bowl, combine flour, cocoa powder, baking powder, and salt, then whisk and set aside.

In a medium bowl, whisk together eggs and sugar until just combined.

Incorporate the melted butter, milk, and vanilla extract into the egg mixture and mix well.

Gradually add the wet ingredients to the dry flour mixture, stirring with a whisk or spoon, then add hot water until everything is fully combined.

Pour the batter into the prepared loaf pan and bake for 39 minutes, or until a toothpick inserted into the center comes out clean with a few moist crumbs. Cool in the pan for 20 minutes, then transfer to a wire rack to cool for another 20 minutes before slicing.