Preheat a panini press or grill pan over medium heat.
In a bowl, mix the shredded chicken with pesto sauce until well combined. Season with salt and pepper to taste.
Slice the ciabatta rolls in half and layer the bottom half with a slice of mozzarella cheese.
Spoon a generous amount of the pesto chicken mixture over the cheese. Add chopped sun-dried tomatoes and fresh basil leaves on top.
Place another slice of mozzarella cheese on top of the filling, then cover with the top half of the ciabatta roll.
Brush the outside of each sandwich with olive oil.
Place the sandwiches in the panini press or grill pan. If using a grill pan, press down with a heavy skillet to flatten the sandwich. Cook for about 4-5 minutes, or until the bread is golden brown and the cheese is melted.
Remove from heat and let cool for a minute before slicing in half.