Combine the broth, nutmeg and horseradish in a small bowl. Melt the butter in a large skillet over medium heat. Add the onions, thyme and salt to the pan. Cook, stirring often, until the onions are golden brown and soft, about 20 minutes. Add the broth mixture and cook another 2 minutes. Let cool slightly.
Slice the bread at 1 1/2" intervals with a large serrated knife, stopping about 3/4 of the way to the bottom. Repeat, making perpendicular cuts, to create a crosshatch pattern in the top of the loaf.
Set the loaf on a parchment-lined rimmed baking sheet. Stuff the onions into the slits then put the cheese slices into the slits. Cover the bread loosely with foil and bake at 350 degrees for 15 minutes. Remove the foil and continue baking until the cheese melts and the bread is toasted, 20 - 25 more minutes. Serve immediately.