Heat 2 tablespoons of olive oil and 2 tablespoons of butter in a large pan over medium-high heat.
Dredge both sides of the chicken in the finely crushed croutons.
Place two chicken breasts at a time in the pan and reduce the heat to medium-low after one minute. Cook for 5 minutes, then flip and cook for an additional 5 to 7 minutes until the internal temperature reaches 160°F. Transfer to a plate, add more butter and oil, and repeat the process with the remaining chicken.
Prepare the pesto while the chicken cooks.
Butter the insides of the bread and sprinkle with garlic salt. Broil the bread open-faced until golden brown, then remove and set aside.
Spread one or two spoonfuls of sauce onto the bottom piece of bread and place the chicken on top.
Cover the chicken with more sauce and add mozzarella cheese.
Place the sandwich under the broiler until the cheese is bubbly, then sprinkle with parmesan and add a smear of pesto. Close the sandwich with the top piece of bread and serve.
