To make doughnuts, place milk, butter, caster sugar, lemon zest, 300ml water and a pinch of salt in a saucepan over medium heat. As soon as mixture starts to bubble, add flour and baking powder, and beat with a wooden spoon until a smooth paste and mixture comes away from the sides of the pan. Remove from heat. Set aside for 5 minutes to cool slightly. Add eggs, 1 at a time, beating well after each addition until smooth and glossy. Cover with a tea towel and set aside for 30 minutes to rest.
Meanwhile, for the caramel, place brown sugar, pared lemon, star anise, cinnamon quill and 3 cups (750ml) water in a pan over medium heat, stirring until sugar dissolves. Increase heat to medium-high and bring to the boil. Cook, for 20-25 minutes until thick enough to coat the back of a spoon. Strain and keep warm.
Heat sunflower oil in a deep saucepan or deep-fryer to 180 degrees C (a cube of bread will turn golden in 30 seconds when oil is hot enough). Using 1 tbs of dough each, roll the dough into 3cm-diameter balls. In batches, deep-fry the doughnuts for 8-10 minutes until golden. Remove with a slotted spoon and drain on paper towel. Repeat with remaining doughnuts.
