Preheat the oven to 400°F.
In a large nonstick skillet, heat the butter. Saute the onion over medium-high heat until soft, about 5 minutes. Add the chard and cook until wilted and the stems are tender, about 5 minutes.
In a small bowl, whisk together the milk and cornstarch. Add to the pan and simmer until slightly thickened, about 5 minutes. Season with the nutmeg and 1 teaspoon salt.
Transfer the greens to a 3-quart ceramic baking dish and sprinkle the cheese over the top, followed by the breadcrumbs. Bake for 15 minutes, until heated through and the top is lightly golden brown.