Cut potatoes into 1/4 inch slices, then quarter each of those. Beat together the cream, milk, flour, garlic, salt and pepper by hand just until well combined.
Coat the inside of a large baking dish with softened butter. Arrange 1/4 of the potatoes on the bottom of the dish; pour some of the cream mixture over the potatoes. Repeat this layering step 3 more times.
Cover the potatoes and bake in a preheated 400º oven for 20 minutes. Uncover and bake another 40 minutes or until the potatoes are starting to brown on top. Sprinkle grated cheese over the top of the potatoes and continue to bake for 5 to 10 minutes or until the cheese is melted and slightly browned and the potatoes are tender. Sprinkle the parsley on top and serve.