Heat oven to 400° F.
Heat 1 tablespoon of the oil in a large saucepan over medium-high heat. Add the onion, celery, and carrots and cook, stirring occasionally, for 3 to 4 minutes. Add the tomatoes and their juices, broth, salt, and pepper. Bring to a boil. Add the Swiss chard and cook, stirring, until wilted, 1 to 2 minutes. Stir in the beans and 1 cup of the Parmesan. Transfer to an 8-by-11-inch baking dish or shallow 2-quart casserole.
Cut the baguette in half crosswise and trim the ends to form two 8-inch portions. Slice each portion lengthwise to make several 1/4-inch-thick slices. Brush the top of each slice with the remaining oil. Arrange the slices, oil-side up, over the casserole, overlapping them slightly. Top with the thyme and the remaining Parmesan. Bake until the bread is golden brown, about 20 minutes.