Preheat the oven to 180°C (160°C for fan assisted ovens)/Gas Mark 4. Grease and line the base and sides of a 20cm square cake tin with baking paper.
Mix the vegetable oil, brownie mix, water and egg together in a bowl until well blended. Spread the mixture evenly in the prepared cake tin and bake for 20-25 minutes or until a round bladed knife inserted into the centre comes out almost clean. Remove from the oven and leave the brownie to cool completely in the tin; about 1 hour.
To make the peppermint icing, sift the icing sugar into a large bowl and add the butter along with the peppermint extract and most of the milk. Add a little green food colouring paste or gel and beat together with a wooden spoon until smooth and creamy, adding the rest of the milk if needed. Beat in more food colouring if the mixture is not green enough. Use a small palette knife to spread the mixture over the cooled brownie square. Chill in the fridge for 15 minutes.
Make the chocolate topping. In a small microwave-proof bowl, microwave the chocolate chips, butter and golden syrup, uncovered, on High for 40-50 seconds, stirring halfway through until melted and smooth. Cool for 2-3 minutes, then spread the topping over the green icing layer. Chill for at least 3 hours.
Use the baking paper to lift the brownie square from the tin. Place on a chopping board and cut into 16 squares, then cut each square diagonally to make 32 triangles to serve. Store any leftover triangles in an airtight container in a cool place for 2-3 days.