Preheat the oven to 375°F. Grease a 9x13-inch baking dish.
In a large skillet, cook the turkey sausage over medium heat until browned, breaking it into crumbles. Drain any excess grease if needed.
Spread the hash browns or diced potatoes evenly in the prepared baking dish.
Sprinkle the cooked turkey sausage over the potatoes, then top with the shredded cheddar cheese.
In a large mixing bowl, whisk together the eggs, Greek yogurt, milk, salt, pepper, and garlic powder until smooth.
Pour the egg mixture evenly over the casserole.
Bake for 40–45 minutes, or until the center is set and a knife inserted into the middle comes out clean.
Let the casserole rest for 5–10 minutes before slicing and serving.