Preheat your oven to 350°F and generously grease a 9x13 inch baking dish with the softened butter, ensuring all sides and corners are coated to prevent sticking.
Spread the cubed bread evenly in the prepared baking dish, then layer the diced ham, chopped onion, and green bell pepper on top, followed by sprinkling the shredded cheddar cheese over everything.
In a large mixing bowl, whisk together the eggs, milk, dry mustard, garlic powder, black pepper, and salt until the mixture is completely smooth and well combined.
Slowly pour the egg mixture evenly over the contents of the baking dish, pressing down lightly with a spatula to ensure all the bread cubes become saturated with the liquid.
Allow the casserole to sit undisturbed for 10 minutes so the bread can fully absorb the egg mixture, which is essential for a cohesive final texture.
Bake uncovered in the preheated oven for 45-55 minutes, or until the top is golden brown and puffed, and a knife inserted into the center comes out clean.
Let the casserole rest on a wire rack for 10 minutes before slicing and serving, which allows it to set properly for clean cuts.