Preheat your oven to 375 degrees Fahrenheit.

Butter the bottom and sides of a 2-quart casserole or gratin dish with 1 tablespoon of softened butter.

In a small saucepan over medium heat, melt 2 tablespoons of butter. Once melted, add the chopped garlic and cook for about 30 seconds until fragrant.

Add the chopped fresh thyme, sage, and 1/2 teaspoon of kosher salt. Cook for another 30 seconds.

Pour in the heavy cream, whole milk, ground cinnamon, and ground nutmeg, and bring to a gentle simmer, stirring occasionally for about 5 minutes.

Remove the saucepan from heat and let the cream mixture cool for a few moments.

In a medium bowl, beat the two large eggs. Gradually whisk in 1 cup of the cream mixture to the eggs, and then return it to the rest of the cream mixture in the saucepan and whisk until combined.

Stir in 1/2 cup of grated Parmesan cheese and add freshly ground black pepper.

Layer the sliced sweet potatoes in the bottom of the prepared dish, slightly overlapping.

Sprinkle kosher salt over the top, then add 2/3 cup of Gruyere cheese followed by 2/3 cup of the cream mixture.

Repeat the layering process two more times, finishing with a layer of cream mixture and top it off with the remaining 1/4 cup of Parmesan cheese.

Cover the dish with aluminum foil, buttering the side that touches the gratin.

Bake the gratin in the preheated oven for 30 minutes.

Carefully remove the foil and bake for an additional 30 minutes, or until the top is golden brown.

Let cool slightly before garnishing with additional fresh thyme.