Heat the oven to 175 C / 350 F with a rack in the middle. Oil the sides of a 23 cm / 9-inch springform pan with 1 tsp olive oil and line the base with parchment.
Sift the flour, cocoa, baking powder, baking soda, and 1/2 tsp fine sea salt into a medium bowl. Whisk to combine.
In a large bowl, whisk the eggs and sugar for 2 minutes until pale and slightly thickened. Whisk in the 150 ml olive oil in a slow stream, then the milk and vanilla, until the mixture looks glossy.
Add the dry ingredients in two additions, whisking just until no streaks remain. Pour in the hot coffee and whisk until smooth. The batter will be thin, about the consistency of heavy cream.
Pour the batter into the pan and tap it on the counter twice to release air bubbles. Bake for 40 minutes, checking at 38, until a toothpick shows a few moist crumbs, the top springs back, and the center reads 205 F / 96 C.
Cool the cake in the pan on a wire rack for 15 minutes. Brush the top with 2 tsp olive oil, sprinkle on the flaky sea salt, then run a knife around the edge and release the ring.
Cool on the rack for 30 more minutes before slicing into 10 wedges. Cutting earlier gives a gummy center.