Preheat oven to fan forced 160ºC. Butter a large rectangular baking dish and set aside.
Place onions into Thermomix bowl and chop for 3 sec/speed 4. Place into large baking dish and set aside.
Place garlic and all cheeses into Thermomix bowl and mill for 8 sec/speed 8. Set aside.
Finely slice half the potatoes and toss them through with the onions, making sure they sit flat in the dish.
Sprinkle with a little cheese, some salt and drizzle with half the cream. Cut the artichoke hearts in half and lay a few across the the top of the potato mixture.
Repeat with remaining layers finishing with cheese. Cover with aliminuim foil, shiny side down and bake for 80 minutes.
Test that the potatoes are cooked with a skewer. Cook in 10 minute increments until you are happy that the potatoes are well cooked.
Increase heat of oven to 180ºC, remove foil and bake a further 20 minutes until golden.
Serve immediately with a little sprinkling of Gremolata as a side dish to roasted meat and fish.