Preheat your oven to 375°F (190°C) and generously grease a 9x13 inch baking dish with butter.

In a large skillet over medium heat, melt the butter and briefly sauté the chicken pieces until they are white on the outside but not fully cooked through, about 3-4 minutes.

In a separate saucepan, combine the heavy cream, milk, minced garlic, thyme, nutmeg, salt, and pepper, bringing the mixture to a gentle simmer over medium-low heat.

Arrange half of the thinly sliced potatoes in an overlapping layer at the bottom of the prepared baking dish.

Distribute the sautéed chicken pieces evenly over the potato layer and sprinkle with one cup of the shredded Gruyère cheese.

Layer the remaining sliced potatoes over the chicken and cheese, arranging them neatly to cover the filling.

Pour the warm cream mixture evenly over the entire dish, ensuring the liquids seep down between the layers.

Top with the remaining cup of Gruyère cheese and cover the baking dish tightly with aluminum foil.

Bake for 40 minutes, then carefully remove the foil and bake for another 20 minutes until the potatoes are tender and the top is golden brown and bubbling.

Allow the gratin to rest for at least 10 minutes before slicing to let the sauce thicken, then serve warm.