Slice the avocado length-wise to get long, thin pieces.
Butter the top side of each piece of bread. Cut a whole in the bread big enough to fit two avocado slices around the outside, and an egg in the center.
Melt a few teaspoons of butter in a large, oven proof skillet over medium high heat.
Add the bread to the skillet and place 2 avocado slices around the outer rim of the circle.
Crack an egg into the center of the circle. Season with a little salt and pepper.
Reduce heat to medium and cook until the bottom of the bread is nicely browned.
Carefully flip to the other side and cook for 2 minutes more, until browned.
Sprinkle 2 Tbsp of cheese over each piece of toast.
Place the skillet in the oven to broil for 1-2 minutes, or until cheese is bubbly.