Let's cook.
Preheat your oven to 375°F (190°C). Grease an 8x8 inch baking dish with the unsalted butter.
Spread the cubed bread evenly in the prepared baking dish. Sprinkle the diced ham and shredded cheddar cheese over the bread.
In a medium bowl, whisk together the eggs, milk, Dijon mustard, salt, and black pepper until well combined.
Pour the egg mixture evenly over the bread, ham, and cheese in the baking dish. Gently press down on the bread to ensure it absorbs the liquid.
Bake for 45 minutes, or until the strata is puffed, golden brown, and a knife inserted into the center comes out clean. If the top browns too quickly, you can loosely cover it with foil for the last 10-15 minutes.
Remove from the oven and let it rest for 5 minutes before serving.
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