Preheat oven to 375°F and grease a 9x13 baking dish.
Brown sausage in a skillet with the onion until sausage is cooked and onion is soft. Drain excess fat.
Stir diced apples into the skillet and cook 2 minutes to soften slightly.
In a large bowl, whisk eggs, milk, salt, pepper, thyme, and melted butter.
Add hashbrowns, cheese, and the sausage-apple mixture to the bowl; mix until combined.
Transfer to the prepared dish and press level. Bake 35–40 minutes until set and top is golden.
Let rest 5 minutes before slicing.