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Butter an 8x8 or 9x13 baking dish. Layer the bun halves cut-side up on the bottom, filling all the gaps.
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In a large bowl, whisk together eggs, milk, cream, sugar, vanilla, cinnamon, salt, and nutmeg until smooth.
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Pour the custard slowly over the bun pieces, making sure they absorb the liquid evenly.
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Let the baking dish sit for 10-15 minutes while the buns soak up the custard.
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Preheat oven to 350°F. Dot the top with butter.
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Bake for 35-40 minutes until the custard is set but slightly jiggly in the center.
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Let rest for 5 minutes before serving.