Let's cook.
In a small bowl, combine the basil pesto and softened cream cheese. Mix until well combined and creamy.
Lay out the four slices of bread. Spread half of the pesto-cream cheese mixture evenly on two slices of bread.
Top the pesto-cream cheese mixture with the sliced cooked chicken breast, dividing it between the two slices.
Evenly distribute the fresh mozzarella cheese over the chicken on both bread slices.
Place the remaining two slices of bread on top to form two sandwiches.
Brush the outside of each sandwich with olive oil.
Preheat a panini press to medium-high heat. If you don't have a panini press, use a large skillet over medium heat.
Place the sandwiches in the panini press and cook for 4-6 minutes, or until the bread is golden brown and crispy, and the cheese is melted. If using a skillet, cook for 3-4 minutes per side, pressing down with a spatula or another heavy pan.
Remove from the panini press or skillet, slice in half, and serve immediately.
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