Add ham to a medium pan and sauté over medium-high heat for a few minutes. Transfer to a bowl and set aside.
Add the white onion and red pepper to the saute pan, and saute for about 4 minutes until cooked. Pour the vegetable mixture into the bowl with the ham. Add the hash browns and cheese to the mixing bowl as well, reserving a little bit of the cheese for topping.
Stir to combine.
In a separate bowl whisk together the liquid eggs with the milk and black pepper - then add it to the has brown mixture and stir.
Pour the mixture into a greased casserole dish, and top with the remaining cheese and some green onions.
Cover the dish with its lid or aluminum foil, and bake for 35-45 minutes, again depending on size of casserole dish and how thick the mixture is. Test doneness by scooping out a bit of the egg that settles on the bottom of the dish. If it resembles scrambled eggs - it's done.
Remove lid or aluminum foil and bake for an additional 10-15 minutes to crisp up the top a bit.
You can add a few more chopped green onions to the top if you wish too.