Thaw the frozen hash browns in the refrigerator overnight or for a few hours before you plan to make the omelet.
In a large skillet, cook the bacon over medium heat until it’s crisp. Remove the bacon to a paper towel to drain, and then crumble it.
Add the potatoes, onion, and green pepper to the skillet with the bacon drippings. Cook and stir over medium heat for 7-10 minutes or until the potatoes are lightly browned and the vegetables are tender.
Beat the eggs in a bowl and add milk, salt, and pepper to taste.
Pour the egg mixture over the hash brown mixture in the skillet. Sprinkle the crumbled bacon on top. Cook the omelet over low heat for 15-20 minutes until the eggs are set. As the eggs set, lift the edges and let the uncooked portion flow underneath.
When the eggs are set, remove the skillet from the heat.
Use a spatula to fold the omelet in half, and then slide it onto a plate.