In a bowl, mix the red onion with the minced beef and season with salt and freshly ground black pepper. Shape the mince into a burger, then insert the mozzarella into the middle of the burger.
Heat a non-stick frying pan. Add the oil and cook the burger for 4-5 minutes on each side, or until cooked through.
Take off the heat and leave to rest for 3 minutes.
Make the courgette fries. Dip the courgettes in the milk, then coat the courgettes in flour.
Heat the oil in a heavy-bottomed saucepan. It is ready when a breadcrumb that is dropped in will sizzle gently in it. (CAUTION: hot oil can be dangerous. Do not leave unattended.) Place the courgettes in the hot oil and deep fry for 4 minutes until golden. Remove with a slotted spoon and drain on kitchen towels.
To serve place the burger on a plate and serve the courgette fries on the side.