Step 1

Heat a skillet over medium heat, then add the onion, oil, thyme and a big pinch of salt, and toss well. Reduce the heat to medium-low and let the mixture cook, tossing onions occasionally, until they turn brown all over, about 20 to 30 minutes. If the onions start to get too dark, turn down the heat, or if they aren't browning fast enough, raise the heat. Taste and add more salt if needed.

Step 2

Meanwhile, lightly grease a 2-quart gratin dish. Cover potatoes with 1-inch of salted water in a large pot. Boil potatoes until fork tender, about 20 minutes. Drain.

Step 3

Mash potatoes with 4 tablespoons butter, Gruyère, sour cream, salt and pepper. Mash in the onions and parsley. Taste and adjust seasoning. Spread potatoes in prepared dish. Cover and refrigerate for up to 3 days.

Step 4

Melt remaining 2 tablespoons butter in a small pot or in the microwave and pour into a small bowl. Stir in breadcrumbs and Parmigiano-Reggiano until coarse crumbs form (crumbs can also be refrigerated for up to 3 days).

Step 5

When ready to cook, heat oven to 400 F. Sprinkle crumbs over top of potato casserole and bake until golden and crisp, 30 to 35 minutes.