Grease a 9x13-inch baking dish with butter or non-stick cooking spray, ensuring the bottom and sides are fully coated.
In the prepared baking dish, combine the torn bread pieces, diced ham, shredded cheddar, chopped onion, and chives, spreading the mixture into an even layer.
In a large bowl, vigorously whisk together the eggs, milk, dry mustard, salt, pepper, and paprika until the mixture is completely smooth and uniform in color.
Slowly pour the egg mixture evenly over the bread and ham in the baking dish, then gently press down on the bread with a spatula to ensure all pieces are submerged and soaking up the liquid.
Cover the dish tightly with plastic wrap and refrigerate for at least 4 hours or preferably overnight to allow the bread to fully absorb the custard.
Preheat your oven to 350°F (175°C) and remove the strata from the refrigerator while the oven heats up.
Uncover the dish and bake for 45 to 55 minutes, until the top is golden brown, the edges are bubbly, and a knife inserted into the center comes out clean.
Let the strata rest on a wire rack for 10 minutes before slicing and serving, which allows it to set for cleaner portions.
