In a small saucepan, combine heavy cream, milk, pressed garlic, and dried thyme. Warm gently for 2–3 minutes (do not boil). Remove from heat and stir in salt and yogurt.
Peel and slice potatoes very thin (about ⅛ inch).
Add olive oil to a baking dish and spread to coat the bottom and sides.
Arrange potatoes in overlapping layers. Pour the cream mixture evenly over. Gently press down so the liquid settles between the layers.
Cover with foil and bake for 40–45 minutes. Remove foil and bake for another 25–30 minutes, until the potatoes are tender and the top is lightly golden.
Let rest for 10–15 minutes before serving. Bon appétit.