Butter a 4¾x9” (12x23 cm) pan. Line the bottom with some parchment paper.
In a large mixing bowl, cream the butter and sugars until very light and fluffy, mix in the vanilla paste. Add the eggs one at a time, and mix just until fully incorporated.
Sift flour and baking powder in a bowl.
Fold in alternately dry ingredients and milk.
Pour ⅔ of the batter into the prepared pan. Mix in cocoa and coffee in the last third of the batter, and pour it on top of the white in the pan. Using a knife “cut” in a zig-zag and up’n down motion down the pan to create a marbled effect.
Bake the cake for 45-55 minutes until a cake tester inserted into the center comes out clean. Turn out onto a cooling rack and leave to cool.