Preheat oven to 350 F/180 C.
Rub a baking 9 inch/23 cm dish with the garlic clove, and then smear with 1 tablespoon of butter.
Peel the potatoes and slice them thinly about 1/8 inch or 3 mm thick. Using a potato slicer will make this job easier, but this can be done by hand as well. Just make sure the potatoes are sliced thinly and about the same thickness. Set aside the sliced potatoes.
Mix the salt, pepper, rosemary and cream together.
Now spread a layer of the potatoes on the baking dish, and pour 1/3 of this cream mixture on top of the potatoes. Add 1 tablespoon of butter and then scatter with 1/3 of the cheese. Repeat this for the 2nd and 3rd layer, and finally top with cheese.
Cover with foil, and bake for 40 to 45 minutes. Remove the foil and bake for another 10-15 minutes until the potatoes are cooked through and are fork tender and the cheese is golden and bubbly.
Rest for 10 minutes before serving.