Heat a skillet over medium heat.
Spread butter evenly on one side of each bread slice.
Place two slices of bread butter-side down in the skillet.
Layer mozzarella cheese, avocado slices, and tomato slices on the bread.
Sprinkle a little salt and black pepper over the filling.
Top with the remaining bread slices butter-side up.
Cook for 3–4 minutes until the bottom turns golden and crispy.
Carefully flip the sandwiches and cook another 3–4 minutes until cheese melts.
Remove from skillet, slice in half, and serve warm.