Preheat the oven to 180°C. Grease two 6-inch baking tins and line the bottoms with parchment paper.
Whisk eggs and sugar together in a large bowl until pale and fluffy.
Add vanilla extract and oil to the egg mixture and mix well until fully combined.
Sift together flour, baking powder, and salt. Fold gently into the wet mixture until smooth. Avoid overmixing, as this can make the sponge dense.
Dissolve cocoa powder in boiling water and add it gradually to the batter. Mix gently until the batter is uniform and glossy.
Divide the batter evenly between the two prepared tins. Smooth the tops with a spatula.
Bake for 30 minutes at 180°C. Check with a toothpick; it should come out clean. Oven temperatures vary, so adjust as needed.
Let the cakes cool in the tins for 10 minutes, then transfer to a wire rack. Allow to cool completely before layering.