Oil a deep 9" x 13" baking dish or casserole. Preheat the oven to 350°.
Wash and dice the onion, celery, mushrooms, kale, and herbs. Dice the fontina and finely grate the Parmesan. Set aside.
Make a custard by first whisking the pumpkin puree and eggs together, then slowing whisking in the milk to combine. Add in about ¾ cup of the Parmesan, the nutmeg, 1 teaspoon salt, and freshly ground black pepper to taste. Set aside.
In a large skillet set over medium-high heat, add half the olive oil or butter. Add the onions and celery and sauted, stirring frequently, until the onions become translucent and soft without browning, about 5-7 minutes. While the onions are softening, in your largest mixing bowl, use your fingers to tear the bread into bite-sized chunks. Remove the crust only if it is especially thick and tough, otherwise include it. Lightly salt the bread and toss it.
When the onions and celery are tender, add them to the bread. Heat the rest of the olive oil or butter in the skillet and sauted the mushrooms until they have released some of their moisture and are beginning to brown, about 5-7 minutes. Add in the garlic, kale and ½ teaspoon or so of salt and a generous amount of pepper and sauted another 2-3 minutes until the kale has softened a little and the mushrooms are well-browned. Add them to the bread and onion mixture in the large bowl. Add the diced fontina if using, and give the ingredients in the bowl a good toss.
Pour the reserved pumpkin custard mixture over the bread and vegetables and gently stir with a rubber spatula, scraping down the sides and bringing the ingredients up from the bottom to evenly coat them with the custard mixture. Tip it out into the prepared baking pan.
Cover the dish tightly with foil. Bake for 45 minutes, remove the dish from the oven and remove the foil. Sprinkle the remaining Parmesan over the top, and bake for another 15 minutes until the cheese is browned and bubbling. Remove from the oven and allow to set for 10 minutes before serving. The pieces cut nicely into squares like lasagne, or can be spooned out with a large spoon.