Caramelized Italian Onion and New Potato Gratin

2 Tbsp. unsalted butter

1 Tbsp. extra-virgin olive oil

2 cups red onion sliced

Kosher salt and freshly ground black pepper

1.5 lbs New Potatoes sliced thin

1-1/2 tsp. chopped fresh thyme

4 oz. grated Parmesan cheese (about 1-1/2 cups)

2 cups whole milk

Pinch freshly grated nutmeg

Position a rack in the center of the oven and heat the oven to 350°F.

Heat 1 Tbsp. of the butter and the olive oil in a 10-inch skillet over medium heat. Add the onions and cook without stirring until beginning to brown, 5 to 7 minutes. Sprinkle with 1/4 tsp. salt and 1/4 tsp. pepper. Reduce the heat to low and continue to cook, stirring and scraping the bottom of the pan frequently with a wooden spoon and spreading the onions evenly over the bottom of the skillet, until golden brown, 30 to 40 minutes. Add 1 Tbsp. water at a time if the onions begin to stick to the skillet. Set aside to cool.

Slice the potatoes into thin rounds (about 1/16 inch thick). Spread about one-third of the potatoes in the bottom of a 3-quart baking dish. Sprinkle with salt, pepper, and half of the thyme. Scatter half of the caramelized onions evenly over the potatoes, and top with one-third of the cheese. Make a second layer with half of the remaining potatoes. Sprinkle with salt and pepper, and top with the remaining thyme and onions. Top with one-third of the cheese. Top with a third and final layer of potatoes.

In a 2-quart saucepan, bring the milk to a simmer. Stir in the nutmeg, and then pour the hot milk evenly over the potatoes. Top with the remaining cheese. Cut the remaining 1 Tbsp. butter into small pieces and scatter on top.

Bake until the potatoes are tender when pierced with a knife and the top is golden brown, 1 hour to 1-1/4 hours. Cover loosely with foil if the top begins to darken too quickly. Let the gratin cool for 10 to 15 minutes before serving.