Preheat the oven to 375 degrees F (190 degrees C) and grease a 9x13-inch baking dish with one tablespoon of unsalted butter.

In a medium saucepan over medium heat, combine the heavy cream, whole milk, minced garlic, fresh thyme, ground nutmeg, salt, and black pepper. Bring the mixture to a gentle simmer, then remove from heat and let it steep for 10 minutes to infuse the cream with flavor.

Using a mandoline or a sharp chef's knife, slice the peeled potatoes and trimmed fennel bulbs into very thin, uniform rounds about 1/8-inch thick.

Arrange half of the sliced potatoes and fennel in alternating, overlapping layers in the prepared baking dish. Pour half of the warm cream mixture evenly over this first layer, then sprinkle with half of the grated Gruyere cheese.

Layer the remaining potatoes and fennel on top, pour the rest of the cream mixture over them, and press down gently with a spatula to ensure the vegetables are submerged. Top with the remaining Gruyere cheese.

Cover the baking dish tightly with aluminum foil and bake for 40 minutes, or until the potatoes are tender when pierced with a fork.

Remove the foil and bake uncovered for an additional 15 to 20 minutes, or until the cheese is bubbling and the top is a deep golden brown. Let the dish rest for 10 minutes before slicing to allow the sauce to set and thicken, then serve warm.