Preheat your oven to 375°F (190°C) and generously grease an 8x8-inch baking dish with the unsalted butter.

Prepare the fennel by trimming off the tough stalks and root ends, then slice the bulbs as thinly as possible using a sharp knife or a mandoline slicer.

In a medium saucepan, combine the heavy cream, whole milk, minced garlic, fresh thyme, kosher salt, black pepper, and ground nutmeg. Bring the mixture to a gentle simmer over medium heat until fragrant, about 3 to 4 minutes, then immediately remove it from the heat.

Arrange half of the sliced fennel in an even layer in the prepared baking dish. Pour half of the warm cream mixture over the fennel, then sprinkle with half of the grated Gruyère cheese.

Layer the remaining sliced fennel on top, pour over the rest of the cream mixture, and finish with an even layer of the remaining Gruyère cheese.

Cover the baking dish tightly with aluminum foil and bake for 35 minutes until the fennel is tender when pierced with a fork.

Remove the foil and bake for an additional 15 to 20 minutes until the top is bubbling and baked to a deep golden brown. Let the dish rest for 10 minutes before serving to allow the cream sauce to thicken slightly.