Preheat the oven to 375°F (180°C).
Butter a casserole dish. Peel and slice in half the garlic clove. Rub the clove all over the buttered dish.
Peel and thinly slice the potatoes and the carrots.
Outdo yourself by carefully and meticulously laying the slices into an intricate and impossible-to-replicate design in an effort to make your dish look like the picture in the cookbook.
Salt, pepper and nutmeg your work of art.
Mix together the cream and milk.
Pour the milk-cream on top and sprinkle with thyme and the grated Parmesan cheese.
Bake for 45 minutes, until golden brown.