Preheat the oven to 180C/350F. Lightly brush a 13”x9” swiss roll tin with melted butter, line the base of the tin with parchment paper, then brush lightly again to stick the paper down evenly. Set aside.
Into a small bowl, sift together the flour and cocoa.
Place the eggs, sugar, baking powder, bicarbonate of soda and salt into the bowl of a stand mixer. Using the whisk attachment, whisk at a medium-low speed for 3 minutes to combine and dissolve the sugar. The mixture will have fine bubbles throughout.
Increase the speed to medium-high and whisk until thickened and pale with fine, foamy bubbles, around 5 minutes of beating time.
Increase the speed again to high and whisk the eggs mixture until pale and doubled in size, another 5 minutes.
Reduce the speed to medium low and drizzle in the melted butter and vanilla, mixing together. Immediately reduce the speed to low and add in the sifted flour and cocoa powder, mixing until nearly combined. Turn the mixer off, detach the whisk attachment and use it to finish folding the flour in by hand, to avoid losing too much air from the mixture.
Carefully pour the mixture evenly over the pan, then gently tip the pan to spread the cake mixture out across the pan. Use an offset spatula to help, if required.
Gently drop the pan twice on your worktop to help level the mixture. Bake until puffed and firm to the touch, but still soft enough to hold a shallow impression when gently poked, about 12 minutes.
Immediately after removing the baked cake from the oven, place on a cooling rack and cover tightly with some foil, crimping around the sides to seal. This keeps the cake moist whilst cooling, so it will roll more smoothly and not crack. Allow to cool to room temperature, about 30-60 minutes.
