Dry out or toast the bread cubes. To dry out, place bread on a rimmed baking sheet and let sit out to dry at room temperature, stirring once or twice, at least 8 hours or overnight. To toast, place on a rimmed baking sheet and bake in a 375°F oven until toasted, stirring halfway through, about 20 minutes total.

Heat the oil in a large frying pan over medium-high heat until shimmering. Add the sausage and onion and cook, breaking up the sausage into small pieces with a wooden spoon, until the sausage is cooked through and the onions are tender, 8 to 10 minutes. Meanwhile, chop the chard stems into ½-inch pieces, thinly slice the chard leaves, and keep the stems and leaves separate.

Add the chard stems to the pan and cook until the stems are softened, 3 to 5 minutes more. Add the chard leaves, garlic, and thyme, and cook until the leaves are wilted and tender, about 4 minutes more. Remove the pan from the heat. Taste and season with salt and pepper as needed.

Place ⅓ of the bread cubes (about 4 cups) in an even layer in a 6-quart or larger slow cooker. Scatter ⅓ of the chard mixture (about 1 cup) and 1 cup of the beans over the bread. Scatter ⅔ cup of the cheese over the entire layer. Repeat with layering in this order in the same amounts: bread, chard mixture, cheese, remaining bread, and remaining chard mixture. Refrigerate the remaining ⅔ cup of cheese. Pour the broth evenly over the top of the panade.

Cover and cook on the HIGH setting for 4 to 6 hours, or on the LOW setting for 8 hours. Sprinkle the reserved ⅔ cup cheese over the top of the panade in the last 15 minutes of cooking. Serve in bowls, garnished with parsley if desired.