Place the chicken breasts between plastic wrap and gently pound them until even in thickness. This helps the chicken cook evenly and prevents dry spots. Season both sides with Italian seasoning, salt, and black pepper.
Heat a skillet over medium heat and drizzle in olive oil. Cook the chicken for about 5 to 7 minutes per side until golden brown and fully cooked. Let it rest for a few minutes before slicing into strips.
Lay out the sourdough slices on a clean surface. Spread pesto on one side of each bread slice and add a thin layer of mayonnaise if you like a creamier sandwich.
Layer sliced chicken, tomato slices, fresh greens, and Swiss cheese onto the bread. Place another slice of sourdough on top to complete the sandwich.
Brush the outer sides of the bread lightly with olive oil. Toast the sandwiches in the skillet over medium heat until both sides are crispy and golden brown while the cheese melts perfectly.
Remove the sandwiches from the skillet and let them cool for one minute. Slice them diagonally for a café-style presentation and serve warm while the cheese is gooey.