Preheat your oven to 350°F (175°C). Grease a 2-quart baking dish to prevent sticking.
Spread the frozen hash brown potatoes evenly at the bottom of your prepared dish. Then, layer the shredded pepperjack cheese, diced ham, and chopped green onions over the hash browns.
In a medium bowl, whisk together the beaten eggs, evaporated milk, black pepper, and salt until fully combined.
Pour the egg mixture evenly over the layered ingredients. If you're preparing it ahead of time, you can cover the dish and refrigerate it for several hours or overnight.
Bake in the preheated oven for 40 to 45 minutes, or 55 to 60 minutes if refrigerated overnight. The casserole is done when a knife inserted into the center comes out clean, signaling that the eggs have set properly.
Let the casserole rest for 5 minutes after baking. This will help the flavors meld together and make serving easier.