Turn your oven on to a high broil. 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.