Preheat the panini press according to the manufacturer's instructions.

Spread basil pesto on one side of each slice of bread.

Layer sliced turkey, mozzarella cheese, and tomato on four slices of bread, then top with the remaining slices, pesto side down.

Brush the outside of each sandwich with olive oil.

Place the sandwiches in the preheated panini press and close the lid.

Cook for about 5 minutes, or until the bread is golden brown and the cheese is melted.

Remove from the press and let cool for a minute before slicing in half.