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Preheat the oven to 350 degrees F. Butter a 9 x 13-inch baking dish.
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Set a 9- or 10-inch skillet over medium/medium-high heat. When hot, add a drizzle of olive oil and about half the mushrooms (they should have lots of room). Cook, undisturbed, 4 - 5 minutes, then flip and cook 2 - 3 minutes more. Remove mushrooms to a plate and sprinkle with sea salt. Repeat for the second batch, adding additional olive oil as needed.
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Edge heat down to medium. Add the remaining olive oil and the onions. Cook about 4 minutes. Add garlic, a sprinkle of sea salt, pepper, red pepper flakes, and kale, and cook until the kale is quite supple, about 7 minutes more. Add sherry, scrape up any brown bits, and fold the mushrooms back in. Remove skillet from heat.
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In a large mixing bowl, whisk the eggs and then whisk in the half and half and 1/2 teaspoon sea salt.
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Scatter half the bread cubes in the baking dish. Pour half the egg mixture over top. Add half the vegetables and half the cheese. Top with remaining bread cubes. Add the remaining egg mixture, vegetables, and all but 1/4 cup of cheese. Press and toss gently with fingertips to combine. If using, add decorative bread slices, pressing them down gently so they get moistened. Top with reserved cheese, and finish with black pepper and a sprinkle of sea salt.
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Cover with foil and bake for 30 minutes. Remove foil, and bake until filling is puffed up and bubbly and the top is golden with crisp edges, 15 - 20 minutes more. Cool 10 minutes, then serve.
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Bread pudding can be assembled up to 1 day ahead of time. Keep it covered in the fridge until you're ready to bake.