Heat a skillet over medium heat.
Spread 1/2 tablespoon of butter on one side of each slice of sourdough bread.
Place one slice of bread, buttered side down, in the skillet.
Layer the cheddar cheese, mozzarella cheese, crumbled bacon, and avocado slices on top of the bread in the skillet.
Season with salt and pepper to taste.
Top with the second slice of bread, buttered side up.
Cook for about 3-4 minutes, or until the bottom slice is golden brown.
Carefully flip the sandwich and cook for another 3-4 minutes, until the other side is golden and the cheese is melted.
Remove from the skillet, slice in half, and serve warm.