In a large pot of boiling water, cook the Swiss chard for 2 minutes; drain. When the leaves are cool enough to handle, squeeze out the excess water. Coarsely chop the chard.
In the same pot, heat the olive oil. Add the onions and thyme and cook over moderately low heat, stirring occasionally, until softened, about 12 minutes. Add the chard and white wine and simmer over moderately high heat until the wine is reduced to approximately 1/4 cup, about 5 minutes. Season with salt and pepper.
Preheat oven to 400 degrees. In a small saucepan, bring the chicken broth to a simmer. Butter a 10x15" baking dish. Line the bottom of the dish with 1/3 of the bread slices, over-lapping the slices slightly and cutting the bread to fit in the bottom of the dish. Top with half of the tomato slices and season with salt and pepper. Spread half of the chard on top, then sprinkle with half of the shredded cheese. Repeat the layering once more and then finish with the remaining bread. Pour the hot broth over the casserole and press with a spatula. Brush the top with the melted butter.
Cover the dish with foil and bake in the upper third of the oven for 1 hour. Uncover the dish and bake for 10 minutes longer, or until the top is browned and crisp. Let the casserole rest at least 10 minutes before serving.
The cooked chard can be made ahead and refrigerated for up to 2 days.