Position a rack in the middle of the oven and preheat to 425 degrees . Bring a large pot of water to a boil, salt it and add the chard (the pot will be packed); boil to wilt, 8 to 10 minutes. Strain the chard in a colander and rinse under cool water. Using a clean kitchen towel, drain and squeeze out any excess liquid. Coarsely chop.
Meanwhile, in a medium saucepan, heat the butter over medium heat. Whisk in the flour for 1 minute. Whisk in the milk; season with salt, pepper and a little nutmeg. Cook until thickened slightly.
Layer half of the chard in a medium casserole, then top with half of the bechamel sauce and half of the cheese; repeat the layers, ending with the remaining cheese. Bake until bubbly, 12 to 15 minutes. Meanwhile, add the bread to the oven to toast briefly.
Rub the toasted bread with the cut sides of the garlic. Top each piece with one-quarter of the chard gratin.