Wash and stem the chard. Save half the stems and slice them thin. Bring 2 quarts of salted water to a boil and cooked the sliced stems for 2 minutes. Add the chard leaves and cook until tender, about 3 minutes. Drain and cool. Gently squeeze out the excess liquid from the stems and leaves and coarsely chop them.
Toss together the breadcrumbs and the melted butter. Toast on a baking sheet in a 350-degree oven, stirring now and then, until lightly brown, about 10 minutes.  Melt 1 ½ tablespoons of butter over medium heat in a heavy-bottomed pan and add the diced onion. Cook over medium heat until translucent, about 5 minutes. Stir in the chard and season with salt. Cook for 3 minutes. Sprinkle with the flour and stir well. Then add the milk and nutmeg and cook for 5 minutes, stirring occasionally. Add more milk if the mixture gets too thick. The chard should be moist but not floating in liquid. Taste and add salt if needed.
Butter a small baking dish. Spread the chard mixture evenly in the dish and dot with the remaining butter, cut into bits. Sprinkle the breadcrumbs evenly over the top. Bake in a 350-degree oven until the gratin is golden and bubbling, 20 to 30 minutes.