Butter bottom and sides of a shallow roasting dish.

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Layer bread, Cheddar cheese, and ham in prepared roasting dish.

Beat milk, eggs, thyme, salt, and black pepper together in a bowl.

Pour egg mixture over bread mixture; cover and refrigerate 8 hours or overnight.

Preheat oven to 350 degrees F (175 degrees C).

Bake uncovered egg mixture in the preheated oven until center is set, about 1 hour. Allow to sit and cool for 15 minutes before serving.