Preheat oven to 350 degrees.

Rub the bottom and sides of a 6-cup gratin dish with the smashed garlic clove.

Mince the garlic and set aside.

Spread half of the softened butter into the prepared gratin dish.

In a medium saucepan, combine half-and-half, salt, pepper, nutmeg, cayenne pepper (if using), potatoes, and minced garlic.

Bring the mixture to a boil over medium-high heat, stirring occasionally.

Reduce heat to low and simmer for 2 minutes.

Pour the potato mixture into the prepared gratin dish, distributing the potatoes evenly.

Gently press down on the potatoes until they are covered by the liquid.

Dot the top of the gratin with the remaining butter.

Bake in the preheated oven for about 1 hour and 15 minutes, or until the top is golden brown, basting once or twice during the first 45 minutes.