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In large pan over medium heat, heat olive oil.
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Add onions and cook until soft, about 5 minutes.
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Add garlic and cook 1-2 minutes.
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Add mushrooms and cook until browned and softened. Season with salt and pepper to taste.
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Stir in rosemary and thyme and cook 1-2 minutes.
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Add kale and sauté until just wilted. Season with salt and pepper to taste.
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In large bowl, combine sourdough cubes and kale/mushroom mixture and mix gently. Set aside to cool.
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In large bowl, beat eggs.
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Add milk and vegetable stock and beat until well combined. Season with salt and pepper as desired.
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Pour egg mixture into bowl with bread mixture and add gruyere cheese. Using spatula, toss together until bread is fully coated.
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Into greased ceramic baking dish, pour bread pudding.
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Cover and refrigerate at least 1 hour and up to overnight.
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When ready to bake, preheat oven to 350 degrees F. Remove dish from refrigerator and let sit out about 30 minutes.
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Remove foil and bake about 45 minutes.
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Serve warm. Top with freshly grated parmesan cheese before serving, if desired.