Preheat the oven to 350°F. Lightly grease a 7½ x 6-inch STAUB rectangular baking dish.
Arrange the 3 frozen hash brown patties in a single layer on the bottom of the baking dish. Break the third patty into pieces as needed to fill any gaps and create the most even potato layer possible.
Sprinkle about one-third of the diced ham over the hash browns.
Sprinkle about one-third of the mozzarella cheese over the ham.
Thinly slice the scallions, separating the white and green parts. Reserve most of the green tops for garnishing after baking.
In a large bowl, whisk together the eggs, half-and-half, garlic powder, salt, and black pepper.
Stir the remaining ham, the scallion whites, most of the green peppers, and a small handful of the sliced scallion greens into the egg mixture.
Carefully pour the egg mixture evenly over the hash browns.
Sprinkle the remaining mozzarella cheese evenly over the top.
Cover the baking dish with foil and bake for 30 minutes.
Remove the foil and continue baking for 15–18 minutes, or until the center is just set. A toothpick inserted into the center should come out moist but without liquid egg.
Broil for 1–2 minutes, watching closely, until the cheese is lightly golden.
Remove from the oven and immediately sprinkle the diced tomatoes and the reserved scallion greens over the top.
Let the casserole rest for 10–15 minutes before serving.