Cook the turkey sausage in a large, deep skillet over medium-high heat until evenly browned and 165°F (74°C) in the center. Drain, crumble, and set aside.
Preheat the oven to 350°F (175°C). In a large bowl, stir together the eggs, green onions, frozen hash browns, milk, and cheddar. Stir in the cooked sausage.
Pour the mixture into a 9 × 13-inch baking pan and spread it evenly.
Bake for 1 hour, until the center is set with no visible liquid egg and reaches 165°F (74°C). Cut into six portions and serve warm.