Preheat your oven to 375°F (190°C) and generously grease a medium-sized baking dish with the softened butter.

Prepare the fennel by cutting off the stalks and fronds, removing the tough outer layer, and slicing the bulbs thinly, about 1/4 inch thick.

In a saucepan over medium heat, combine the heavy cream, whole milk, minced garlic, thyme, salt, pepper, and nutmeg.

Bring the cream mixture to a gentle simmer, then remove it from the heat and let it steep for 5 minutes to infuse the flavors.

Arrange half of the sliced fennel in an even layer at the bottom of the buttered baking dish.

Pour half of the warm cream mixture over the fennel and sprinkle with half of the grated Gruyère cheese.

Layer the remaining fennel slices on top, followed by the rest of the cream mixture and the remaining cheese.

Cover the dish loosely with aluminum foil and bake for 30 minutes to allow the fennel to steam and become tender.

Remove the foil and bake for another 20 minutes until the top is bubbly and golden brown.

Let the dish rest for at least 10 minutes before serving to allow the sauce to thicken slightly.