Preheat oven to 350 degrees Fahrenheit (180 degrees Celsius). Butter a 9- x 13-inch (20- x 30-centimeter) baking dish or disposable pan.

Heat a medium-sized pot over high heat. Add four tablespoons butter, onion, and salt.

Stir continuously for six to eight minutes so that the butter browns instead of burning. The onions will lightly caramelize as the butter browns and becomes foamy.

Add the wine and stir. Cook for two minutes until the mixture slightly reduces.

Add heavy cream and milk. Bring the mixture to a boil and immediately remove from heat.

Layer a third of the potatoes in the bottom of the prepared baking dish.

Ladle one cup of the onion-cream mixture over the potatoes. (Use a fork to spread the onions evenly over the potatoes.)

Sprinkle two tablespoons of shredded cheese on top of the onion-cream mixture.

Top with a second layer of potatoes, onion-cream mixture, and two more tablespoons of cheese. Repeat layering and sprinkle the remaining cheese evenly over everything.

Cut up the reserved half a teaspoon of butter into little pieces and dot over the top of the cheese.

Cover pan tightly with foil and place in the oven. Bake covered for one hour, then uncover and bake another 20 minutes until golden and bubbly.

Remove from oven and allow to cool for five minutes before serving.