In a saucepan, cook the parsnips in the milk with a little salt and pepper until they are just tender and the milk is almost completely gone. Transfer to a large bowl and set aside.
Preheat oven to 190°C (375°F).
In a skillet, sweat the leek in the butter without browning and add to the bowl with the parsnips. Add the caraway seed and mustard, toss gently and transfer the mixture to a gratin dish.
Pour the cream over the vegetables, then sprinkle with the Mozzarellissimaand Parmesan cheeses.
Bake in the middle of the oven for 30 minutes or until the cheese is golden and bubbly.