Mix eggs, sour cream, milk, salt, and pepper together in a bowl and set aside.
Mix hash browns, ham, Cheddar cheese, green onions, and bell peppers together in another bowl. Transfer to a 9x13-inch baking pan and mix in egg mixture well; it may appear watery but hash browns will absorb most of it by morning. Cover with plastic wrap and refrigerate, 8 hours to overnight.
Preheat the oven to 400 degrees F (200 degrees C).
Bake in the preheated oven until top is browned and eggs are set, about 55 minutes.