Heat pan to a low heat while spreading butter on each slice of bread. Fry open face until the cheese is melted. While it cooks, heat another nonstick skillet to medium heat.
Cook eggs sunny side up in the skillet. Set aside and heat the olive oil in the skillet to a medium heat and cook hash browns according to the instructions on the package.
Once the cheese is melted, put the pieces on bread together and transfer to plates. smash one half of the avocado on the top of each sandwich and sprinkle on the sea salt and pepper.
Top with egg and hash browns. Sprinkle on salt and pepper and cut in half.