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1
Place a medium saute pan over medium heat, drain excess water from leeks, and add to pan. Season with salt, and saute until leeks begin to soften, about 5 minutes, then reduce heat to medium-low. (They'll release liquid as they cook.) Stir in butter. Cover and cook, stirring occasionally, until leeks are very soft, about 30 minutes. Adjust salt and pepper to taste.
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2
Heat oven to 350u00b0 F. While leeks are cooking, spread bread cubes on a baking sheet and bake until dry and pale gold, about 20 minutes, turning pan about halfway through. Transfer to a large bowl, leaving the oven on.
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3
Add leeks, chives, and thyme to the bowl of bread; toss well. In another large bowl, lightly whisk the eggs, then whisk in milk, cream, a generous pinch of salt, pepper to taste, and a pinch of nutmeg.
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4
Sprinkle 1/4 cup shredded cheese in bottom of a 9- by 13-inch baking pan. Spread 1/2 of bread mixture in pan, and sprinkle with another 1/4 cup cheese. Spread remaining bread mixture in pan, and sprinkle with another 1/4 cup cheese. Pour in enough milk mixture to cover bread, and gently press on bread so milk soaks in. Let rest 15 minutes.
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5
Add remaining milk mixture, letting some bread cubes protrude. Sprinkle with salt and remaining cheese. Bake until pudding is set and top is brown and bubbling, about 1 1/2 hours. Serve hot.