In a large skillet over medium-high heat, sauté the sausage meat, breaking it up, until the sausage is cooked through, about 6 to 8 minutes. Drain the fat and transfer the cooked sausage meat to a bowl; set aside., Return the pan to the burner, and heat the butter until it melts. Add the onion and mushrooms and cook until they start to soften, about 5 minutes., Add the garlic, 1/2 teaspoon of the salt, and herbes de Provence, cooking for another minute or two until fragrant., Add the white wine or stock to deglaze the pan, and cook until almost completely reduced., Transfer the vegetables to the bowl with the sausage, and allow to cool to room temperature., Toss the meat/vegetable mixture with 1 1/2 cups of the cheese and all of the bread., Spread the mixture into a buttered 9" x 13" pan or 3-quart baking dish; set aside., Whisk the eggs and yolks in a large bowl. Add the remaining 1/2 teaspoon salt, milk, and cream, continuing to whisk., Pour the egg mixture into the pan, cover, and refrigerate for at least 1 hour or up to overnight., Preheat the oven to 325°F., Top the pudding with the remaining 1/2 cup of cheese. Bake the pudding for 55 to 65 minutes, until it's puffed, lightly browned, and a knife inserted in the center comes out clean., Let the pudding cool for 15 minutes or so, and serve warm., Wrap any leftover pudding tightly with plastic and refrigerate. Reheat individual servings in the microwave; or the whole pan, covered with foil, in a 250°F oven.