Butter the bread slices on both sides (use the whole stick), then cut them into 3/4-inch squares. (Leave the crust on.)
Beat the eggs in a large bowl until foamy, then gradually whisk in the milk.
Alternate layers of bread and Cheddar in a low 2-quart oval baking dish, starting with the bread and ending with Cheddar (4 layers total). Pour in the egg mixture, and press the bread and Cheddar down into the egg. Refrigerate overnight, covered, so the bread soaks up the liquid.
About 1 1/2 hours before serving, position a rack in the center of the oven and preheat to 175°C. Bake until puffed, golden and cooked through, about 1 hour. Serve hot or warm.
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