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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.
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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.
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Add the garlic, 1/2 teaspoon of the salt, and herbes de Provence, cooking for another minute or two until fragrant.
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Add the white wine or stock to deglaze the pan, and cook until almost completely reduced.
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Transfer the vegetables to the bowl with the sausage, and allow to cool to room temperature.
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Toss the meat/vegetable mixture with 1 1/2 cups of the cheese and all of the bread.
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Spread the mixture into a buttered 9" x 13" pan or 3-quart baking dish; set aside.
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Whisk the eggs and yolks in a large bowl. Add the remaining 1/2 teaspoon salt, milk, and cream, continuing to whisk.
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Pour the egg mixture into the pan, cover, and refrigerate for at least 1 hour or up to overnight.
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Preheat the oven to 325°F.
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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.
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Let the pudding cool for 15 minutes or so, and serve warm.
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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.