In a large skillet over medium heat, brown the sausage until no longer pink, about 5-7 minutes. Break it up with a wooden spoon as it cooks for even browning.
Add the diced onion and bell pepper to the skillet with the cooked sausage. Sauté until softened, about 4-5 minutes.
In a large bowl, whisk together eggs, milk, garlic powder, dried thyme, smoked paprika, salt, and pepper until well combined.
Grease a 9x13-inch baking dish. Spread the thawed hash browns evenly across the bottom. Layer the sausage and vegetable mixture on top, then sprinkle with 1½ cups of the shredded cheese.
Pour the egg mixture evenly over everything.
Cover the baking dish with plastic wrap and refrigerate for at least 8 hours or overnight.
When ready to bake, preheat your oven to 350°F (175°C). Remove the casserole from the refrigerator while the oven preheats (about 20 minutes) to take the chill off.
Bake uncovered for 35 minutes, then sprinkle the remaining ½ cup of cheese on top and bake for an additional 10 minutes until the center is set and the top is golden brown.
Let the casserole rest for 5-10 minutes before serving. Garnish with sliced green onions just before bringing it to the table.