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Cube day-old bread into 1-inch pieces and spread on a baking sheet to dry slightly. Shred cheeses and chop fresh herbs.
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Whisk together eggs, whole milk, Dijon mustard, salt, pepper, and nutmeg in a large bowl until thoroughly mixed. Add most of the fresh herbs.
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Pour melted butter into the bottom of a 9x13 baking dish. Layer half the bread cubes, pour a third of egg mixture over, add half the cheeses (and optional meat), then remaining bread, remaining egg mixture, and top with remaining cheese.
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Cover tightly with plastic wrap and refrigerate overnight (8-24 hours) so the bread absorbs the custard.
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Remove from refrigerator and let sit on counter while oven preheats to 350°F (about 10 minutes).
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Bake uncovered for 40-45 minutes until top is golden brown and a knife inserted in center comes out clean.
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Let rest 10 minutes before serving. Cut into squares or scoop like lasagna.