Preheat the oven to 180C/160C Fan/Gas 4 and grease a 25cm/10in Bundt tin with butter. Add some flour and tilt to dust thoroughly, tapping out the excess.
To make the cake, put the carrots, oil, eggs, vanilla and caster sugar in a blender or food processor. Blend until completely smooth. Pour the carrot mixture into a large bowl then sift over the flour. Add the baking powder and salt and fold until well combined. Pour the mixture into the tin and bake on the middle shelf for 40–45 minutes, until a skewer poked into the centre of the cake comes out clean. Leave the cake to cool in the tin for 10 minutes, then transfer to a wire rack to cool completely.
To make the glaze, put the milk, butter and vanilla in a small saucepan. Place over a low heat until the butter has melted, then add the cocoa and icing sugar. Increase the heat and whisk until it comes to a boil. Simmer for 1–2 minutes, whisking constantly, then take off the heat. Leave to cool until it becomes a thick glaze. Drizzle the glaze evenly over the top of cake then leave to set.