1. Cook the pasta in salted boiling water according to the instructions on the package. Then drain them.
2. Wash and cut the broccoli into florets, then cook them in salted boiling water for 7 to 8 minutes. Then drain them and plunge them into cold water.
3. Meanwhile, prepare the béchamel sauce. In a saucepan, heat a little milk and dissolve the cornstarch in it. Add the remaining milk, salt, pepper, and nutmeg, then let it thicken for a few minutes while stirring.
4. In a bowl, put the drained pasta, then add the béchamel sauce, grated Parmesan cheese, and mix well. Then add the broccoli and ham, and mix everything together.
Pour into a gratin dish, sprinkle with grated Gruyère cheese, and bake at 190°C for 20 to 25 minutes.