Preheat oven to fan forced 160ºC. Butter a large rectangular baking dish or several smaller individual ramekins and set aside.
Place onions into Thermomix bowl and chop 3 sec/speed 4. Place them large mixing bowl and set aside.
Place garlic and all cheeses into Thermomix bowl and mill 8 sec/speed 8. Set aside in a separate bowl.
Finely slice half the potatoes and toss them through the onions.
Mix with a little of the grated cheese, some salt and drizzle with half the cream. Cut the drained artichoke hearts in half and toss through the potato mixture.
Divide this mixture between your prepared baking dishes. Cover with aluminium foil, shiny side down and bake for 80 minutes if doing a single gratin or 60 if doing individual gratins.
Test that the potatoes are cooked with a skewer. Cook in 10 minute increments until you are happy that the potatoes are well cooked. (There is literally nothing worse than a crunchy gratin!)
Increase heat of oven to 180ºC, remove foil and bake a further 20 minutes until golden.
You can reduce the cream content of this dish by replacing some of the cream with a vegetable or chicken stock. There must be plenty of liquid in order to cook the potatoes.
Serve immediately with a little sprinkling of Gremolata as a side dish to roasted meat and fish.