Preheat the oven to 350 degrees F. Combine the broth and nutmeg in a small saucepan and bring to a simmer. Remove from the heat and stir in the horseradish and 1/2 tablespoon butter.
Melt the remaining 4 tablespoons butter in a large skillet over medium heat. Add the onions, thyme and 3/4 teaspoon salt and cook, stirring often, until the onions are golden brown and soft, about 20 minutes. Let cool slightly, then stir into the broth mixture.
Slice the bread at 1 1/2-inch intervals with a large serrated knife, stopping about three-quarters 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 gruyere and onions into the slits, breaking the cheese into smaller pieces, if necessary. Pour any remaining broth mixture into the slits. Cover the bread loosely with foil and bake until warm, about 15 minutes. Remove the foil and continue baking until the cheese melts and the bread is toasted, 20 to 25 more minutes. Sprinkle with parsley.