Heat a skillet over medium heat.
Butter one side of each slice of sourdough bread.
Place two slices of bread, butter side down in the skillet.
Layer the mozzerella cheese, avocado slices and tomato slices on the top of the bread in the skillet.
Add salt and pepper to taste.
Top with fresh basil leaves if using.
Place the remaining slices of bread on top, butter side up.
Cook until the bread is golden brown and the cheese is melted, about 3-4 minutes per side.
Press down gently with a spatula to help the cheese melt the sandwich to stick together.
Remove from the skillet, let it cool for a minute and then slice and serve.