Heat a skillet or grill pan over medium heat.
Lightly brush one side of each bread slice with olive oil or butter.
Place one bread slice, oiled side down, onto the skillet.
Spread mayonnaise evenly over the bread if using.
Layer cooked chicken, avocado slices, and cheese on top.
Season lightly with salt and black pepper.
Top with the second bread slice, oiled side facing up.
Cook until the bottom is golden and cheese begins to melt.
Flip carefully and cook the other side until golden and fully melted.
Remove from heat, slice, and serve warm.