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Heat the oven to 180C/160C fan/gas 4. Oil the base and sides of a 33 x 23cm roasting tin that’s at least 2.5cm deep. Line with baking parchment. Combine the flour, cocoa powder, baking powder, sugar and a good pinch of salt in a large bowl. Break up any sugar lumps with a whisk.
Whisk the oil together with the milk, vanilla and eggs in a jug, and pour into the dry ingredients, then stir in the chocolate chips. Stir well using a spatula until there are no pockets of flour. Pour the mix into the prepared tin and bake for 25-30 mins until a skewer inserted into the centre comes out clean. If any wet mix clings to the skewer, return to the oven for 5 mins, then check again. Leave to cool in the tin for at least 20 mins.
Meanwhile, make the icing. Melt the butter, then remove from the heat and stir in the icing sugar, cocoa powder and milk. The icing will be very runny, but will thicken a little as it cools. (If the icing has thickened too much before the cake has cooled, reheat it slightly to make it easier to pour.)
Pour the chocolate icing over the cake and leave until it has set before slicing into squares.