Preheat oven to 325F. Lightly coat a 9-in. springform pan with olive oil and line the bottom with parchment paper.
Pour boiling water over cocoa powder and whisk to combine. Whisk in vanilla. Reserve.
Stir flour with baking soda and salt in a small bowl and stir until uniform.
Combine sugar with eggs and olive oil in the bowl of a stand mixer. Beat on high until mixture is fluffy and pale yellow. Scrape in cocoa mixture and beat until smooth. Gradually add flour mixture and beat until combined. Pour batter into prepared pan.
Bake in centre of oven until a cake tester inserted into centre of cake comes out almost clean, about 50 min. Let cool in pan for 10 min, then run a knife around the sides of the pan and release sides from base. Remove cake from pan and set onto a rack to cool completely. Peel off parchment paper before serving.