Peel the potatoes and carrots and cut them into large pieces. Wash the broccoli and cut into florets.
Put the vegetables in a saucepan and fill with water until everything is just covered. Salt the contents, bring to the boil and cook over a medium heat for 20 minutes. Then drain the vegetables and let them evaporate for 5 minutes.
In the meantime, bring the milk to the boil and add the parmesan until it melts. Season the mixture with salt, pepper and nutmeg and stir into a homogeneous sauce.
Add the parmesan milk sauce to the vegetables and mash to a puree.