Pre-heat the oven to Gas Mark 6, 200°C, 400°F.
Cook the penne in salted boiling water, making sure to keep it al dente. Drain and return it to the saucepan, off the hob. Add the milk and ⅓ of the béchamel sauce and mix.
Meanwhile, chop the courgettes into small pieces. Cook on a high heat for 5 minutes in a large frying pan with 2 tbsp oil, stirring regularly. Season and put in a colander then leave to drain. Chop the meat into small cubes then brown in the frying pan with 1 tbsp oil. Sprinkle with the oregano and take off the heat when it is thoroughly browned. Add the courgettes and season to taste.
Spread half the penne in an oven dish. Cover with the courgette and meat mixture, then the mozzarella. Spread out the rest of the penne on top, cover with the rest of the béchamel sauce and sprinkle the hard cheese over the top.
Cook in the oven for 10 minutes until golden. Serve hot accompanied by a salad.