Preheat the oven to 375°F (190°C). Generously butter a 9x13-inch (or similar 3- to 3.5-quart) baking dish with 1 tablespoon unsalted butter and set aside.

Wash and slice potatoes

Peel the russet potatoes (peeling optional if you prefer skin on). Using a mandoline or a very sharp knife, slice the potatoes into 1/16 to 1/8-inch (about 1.5–2 mm) thin even slices. Rinse the slices briefly in cold water to remove excess surface starch, then drain and pat dry with a clean kitchen towel or paper towels.

Cream Mixture

Infuse cream

In a medium saucepan, combine 2 cups heavy cream, 1 cup whole milk, 2 lightly crushed garlic cloves (smash with the side of a knife but keep intact), 1 tablespoon fresh thyme (or 1/2 tsp dried), 1 bay leaf, 1 teaspoon grated or ground nutmeg, 1.5 teaspoons salt, and 1 teaspoon freshly ground black pepper. Warm the mixture over medium-low heat until it is steaming and small bubbles form at the edge (do not boil). Reduce heat to low and simmer gently for 5 minutes to allow flavors to infuse.

Remove aromatics

Remove the saucepan from the heat. Discard the bay leaf and garlic cloves (or mince the garlic finely and return it if you prefer a stronger garlic presence). Keep the warm cream mixture nearby.

Assemble & Bake

Layer potatoes

Arrange a single, slightly overlapping layer of potato slices across the bottom of the buttered baking dish, covering it evenly. Sprinkle about one-third of the grated Gruyère over the first layer. Repeat with a second layer of potato slices, another third of the Gruyère, and continue until all potato slices are used, reserving about 1/3 cup of Gruyère for the top. Aim for 4–6 thin layers depending on potato thickness.

Add cream

Carefully pour the warm cream mixture over the layered potatoes so it settles between the slices. The liquid should come just up to the top layer of potatoes but not fully submerge them. Gently press the potatoes down with a spatula to encourage even distribution of cream.

Top with cheese

Sprinkle the remaining Gruyère evenly over the top layer of potatoes, then dust the surface with the 1 tablespoon grated Parmesan for a golden crust.

Bake

Cover the dish loosely with aluminum foil and bake in the preheated 375°F (190°C) oven for 40 minutes. After 40 minutes, remove the foil and continue baking for an additional 20–30 minutes until the top is golden brown, the cream is bubbling around the edges, and a knife inserted into the center meets little resistance — potatoes should be tender.

Rest

Remove the gratin from the oven and let it rest for 10–15 minutes. Resting allows the cream to thicken and makes slicing cleaner.

Finishing

Before serving, sprinkle the chopped fresh parsley over the top if using. Slice into portions and serve warm.