Step 1

In a small saucepan, combine cream, milk, garlic, shallots, nutmeg, thyme, peppercorns, and salt. Bring to a boil, then remove from heat, cover, and let steep for 1 hour.

Step 2

Return milk mixture to boil, then strain into a large heatproof bowl, pressing gently on the solids.

Step 3

Using a mandoline, slice the potatoes crosswise 1/8 inch thick, directly into the hot milk mixture. Stir the potatoes to fully coat.

Step 4

Preheat oven to 300°F (150°C). In a small bowl, combine the Gruyère and Parmigiano-Reggiano cheeses.

Step 5

Grease a 2-quart baking dish with the butter. Lay the sliced potatoes in one even layer, then sprinkle with the cheese mixture. Repeat layering potatoes and cheese until all the potatoes have been used and half the cheese mixture remains; leave the top layer without cheese. Pour any remaining milk mixture over the layered potatoes.

Step 6

Bake until the potatoes have become tender and the surface is lightly golden brown, about 1 1/2 hours. Top with reserved cheese mixture, switch the oven to broil, and broil until evenly browned on top. Allow the gratin to rest 30 minutes before serving.