Preheat your oven to 160°C (325°F). Peel the potatoes and slice them into thin, even rounds, approximately 2–3 mm thick. A mandoline slicer helps create uniform slices, but a sharp knife works well too. Avoid soaking or rinsing the slices after cutting, because their surface starch helps thicken the sauce.
Add the cream, milk, minced garlic, salt, black pepper, and nutmeg to a saucepan. Warm gently over medium-low heat until steaming, stirring occasionally. Do not allow the mixture to boil vigorously. Remove from the heat once the garlic becomes fragrant.
Grease your baking dish generously with butter. Arrange the potato slices in overlapping layers, seasoning lightly between layers if needed. Sprinkle with thyme if desired. Continue until all the potatoes are used, keeping the layers relatively even for consistent cooking.
Slowly pour the warm cream mixture over the layered potatoes. Gently press the potatoes down with the back of a spoon so the liquid settles between the slices. The cream should come close to the top layer without completely drowning the dish. Dot the surface with the remaining butter.
Cover the dish loosely with foil and bake for 40–45 minutes. Remove the foil and continue baking for another 20–30 minutes, or until the potatoes are completely tender and the top is golden brown. Cooking time depends on the thickness of the slices and the depth of your dish.
Remove the dish from the oven and let it rest for 10–15 minutes. This allows the sauce to settle and makes the potatoes easier to portion. Garnish with a little fresh thyme or black pepper, then serve warm alongside your favorite main course.