Preheat the oven to 375°F (190°C).
Combine in a saucepan the heavy cream, milk, minced garlic, thyme, salt, black pepper, and nutmeg. Heat this mixture until it’s just simmering, then remove it from the heat.
Layer half of the thinly sliced butternut squash in a baking dish. Pour half of the creamy sauce over these slices and sprinkle with half of the shredded Gruyere cheese.
Repeat with the remaining butternut squash slices, followed by the rest of the cream mixture and another sprinkle of Gruyere cheese.
Mix in a small bowl the bread crumbs with the remaining Gruyere cheese, then sprinkle this topping over the gratin.
Cover the baking dish with foil and bake for 30 minutes.
Uncover and bake for an additional 15 minutes until the top is golden and bubbly.
Cool for a few minutes before serving.