In a large bowl, whisk the cocoa powder and hot coffee until smooth.
Add the chocolate and stir occasionally until fully melted and mostly cooled, about 1 minute.
Vigorously whisk in the extra-virgin olive oil until smooth.
Add the sugar and whisk until smooth, then add the eggs, sour cream and vanilla, breaking each yolk before whisking until very smooth.
Sift in the flour, baking powder, baking soda and salt. (If you don’t have a sieve, you can whisk these dry ingredients in a separate bowl, then add to the wet ingredients.) Whisk just until incorporated and no flour streaks remain. The batter will be thin.