Position a rack in the center of the oven and heat the oven to 350°F.
Heat 1 Tbs. 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 Tbs. water at a time if the onions begin to stick to the skillet. Set aside to cool.
Peel the potatoes. Using a mandoline or sharp knife, 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 Tbs. butter into small pieces and scatter on top.
Bake until the potatoes are tender when pierced with a paring 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.
Make Ahead Tips
You can make this up to one day in advance. Once cool, cover and refrigerate. Let come to room temperature for about an hour before reheating in a 350°F oven, covered loosely with foil until warmed through, about 20 minutes.
nutrition information (per serving):
11, Fat Calories
100, Saturated Fat
9, Monounsaturated Fat
29, Polyunsaturated Fat
Photo: Scott Phillips