Heat oil in a medium skillet over medium heat.
Add hash browns and cook for a few minutes until heated through, stirring occasionally.
Chop pepper and onion. Add to potatoes.
Cover and cook over medium heat for 6 to 7 minutes, stirring occasionally.
In a medium bowl, whisk together eggs, milk, salt, and pepper. Pour evenly over hash browns, poking the potatoes with a spatula in several places to help the mixture seep through to the skillet.
Turn heat down to medium-low, cover, and cook for 6 to 7 minutes until eggs are just about set.
Sprinkle cheese over top, then cover again and cook for another 2 to 3 minutes until cheese is melted.
Loosen edges and cut into wedges.
Serve with strawberries on the side.