Preheat the oven to 400 degrees . In a large pot of boiling salted water, cook the chard stems until crisp-tender, 4 minutes. Add the leaves; cook until wilted, 5 to 10 seconds. Drain; let cool. Squeeze out excess liquid; transfer to a shallow 2-qt. baking dish, separating clumps.
In a saucepan, melt 1/2 tbsp. butter over medium. Add the shallot; cook, stirring, until soft, 2 minutes. Add the cream and nutmeg; stir until mixture starts to boil. Add all but 2 tbsp. cheese. Stir until melted; pour over the chard.
In a saucepan, melt the remaining 1 1/2 tbsp. butter. In a bowl, toss the bread and butter; season. Scatter the bread and remaining cheese over the chard. Bake 20 minutes.