Preheat your oven to 375°F (190°C). Lightly grease a 9x13 inch baking dish with butter or cooking spray; this helps prevent sticking and makes cleanup easier.

In a large skillet over medium-high heat, cook the ground breakfast sausage, breaking it up with a spoon, until it's browned and cooked through, about 5-7 minutes. Drain any excess grease from the skillet, then transfer the cooked sausage to a large mixing bowl.

In the same skillet (no need to clean it), melt the butter over medium heat. Add the finely chopped onion and bell pepper and cook until they soften, about 5 minutes. Add these sautéed vegetables to the bowl with the cooked sausage.

Add the thawed hash browns, 1.5 cups of the shredded cheddar cheese, salt, and black pepper to the bowl with the sausage and vegetables. Stir everything together gently to combine all the delicious flavors.

In a separate medium bowl, whisk together the eggs and milk until they are well combined and slightly frothy. This creates the binder for your casserole.

Pour the hash brown mixture evenly into your prepared baking dish. Carefully pour the whisked egg mixture over the top, making sure it's distributed evenly so every bite gets some eggy goodness. Bake uncovered for 30 minutes.

Remove the casserole from the oven and sprinkle the remaining 0.5 cup of shredded cheddar cheese over the top. Return it to the oven and bake for another 10-15 minutes, or until the cheese is melted and bubbly, the casserole is set, and the edges are golden brown. A knife inserted into the center should come out clean.

Let the casserole rest for 5-10 minutes before slicing and serving. This crucial step allows the casserole to set up properly, making for cleaner cuts and easier serving.