Preheat the oven to 400 degrees (F).

Melt the butter in a large pot or dutch oven over medium-high heat. Add the shallots and sauté until softened and begin to caramelize, about 10 minutes.

Add the garlic and thyme and continue cooking for another minute, or until fragrant.

Stir in the cream, broth, salt, black pepper, nutmeg, cayenne pepper, and dijon mustard and cook for 2 minutes, stirring almost constantly.

Add in the potatoes and bring to a simmer. Continue cooking until the potatoes are just fork-tender, about 10 minutes.

As neatly as possibly, scrape the potato mixture into a shallow 9x13-inch baking dish (or similar capacity).

Sprinkle the cheeses evenly over the potatoes, starting with the fontina, then adding the gruyere, and finishing with the parmesan. Bake until bubbling and golden brown, about 15 to 18 minutes. Sprinkle with a few thyme springs, if desired.

Let sit for 10 minutes before serving.