How to Make It
Fill a large bowl with water. Peel the salsify and trim the ends. Transfer the salsify to the water as you peel it. Using a mandoline or the slicing blade in a food processor, slice the salsify 1/4 inch thick. Return the salsify to the water to keep it white.
In a large soup pot, melt the butter. Add the flour and cook over moderate heat for 2 minutes, whisking constantly. Add the half-and-half and bring to a boil, whisking constantly. Cook, whisking, for about 3 minutes, or until the half-and-half is slightly thickened. Season with salt, pepper and nutmeg. Drain the salsify and pat it completely dry. Add the salsify to the pot and cook over moderate heat, stirring occasionally, until tender, 25 to 30 minutes.
Preheat the oven to 400° and position a rack in the upper third. Pour the salsify mixture into a 9-by-13-inch baking dish and sprinkle with the cheeses. Bake for about 20 minutes, until the cheese is melted and the gratin is bubbling. Preheat the broiler and broil the gratin for about 5 minutes, or just until the cheese is golden and crusty. Let the gratin stand for 10 minutes before serving.