Adjust oven rack to middle position and heat oven to 250°F. On a rimmed baking sheet, spread bread in an even layer and bake, stirring occasionally, until dried and crisp, 30 to 45 minutes. Let croutons cool completely.
In a Dutch oven or large pot, butter over medium-low until butter is melted. Add pancetta and cook until browned but still slightly chewy and fat is rendered, 6 to 8 minutes.
Stir in onion and salt and cook over medium heat until softened and lightly browned, 6 to 8 minutes. Stir in garlic and caraway seeds and cook until fragrant, about 1 minute.
Add cabbage, broth, and bay leaves and stir to combine. Bring to a boil, then reduce heat to low, cover, and simmer until cabbage is tender, 30 to 45 minutes.
Adjust oven rack to 6 inches from upper broiler coils and heat broiler on high. Discard bay leaves and spread half of cabbage mixture evenly in the bottom of a 9-by-13-inch broiler-safe baking dish, then top with half of the croutons. Repeat the layering with the remaining cabbage mixture, topping it with the croutons. Using a wide flat spatula, gently press down on croutons to submerge and saturate. Sprinkle fontina cheese evenly over top. Broil until cheese is melted and spotty brown, 2 to 4 minutes. Sprinkle with parsley and serve.
