Preheat your oven to 175°C (350°F) and grease the cake pan, lining the bottom with a circle of parchment paper.
In a large bowl, whisk together the olive oil and sugar until the mixture is fully combined and smooth.
Add the eggs one at a time, whisking vigorously after each addition until the batter looks emulsified.
Stir in the vanilla extract.
Sift the flour, cocoa powder, baking soda, and salt directly into the bowl.
Gently fold the dry ingredients into the wet mixture using a spatula until just a few streaks of flour remain.
Pour in the boiling water and stir slowly until the batter is thin, glossy, and completely uniform.
Pour the batter into the prepared pan and bake for 30 to 35 minutes, or until a toothpick inserted into the center comes out with just a few moist crumbs attached.
Allow the cake to cool in the pan for 10 minutes before transferring it to a wire rack to cool completely.