Preheat the oven to 450 F and arrange a sheet tray with parchment paper.
Whisk the olive oil, thyme, lemon juice, salt, and pepper together in a bowl.
Coat the pear slices in the oil mixture and arrange on sheet tray.
Coat chicken cutlets in oil mixture, adding more thyme or oil as needed, and arrange on the sheet tray.
Roast until chicken registers 165 F, about 15 minutes. Pears will be very soft. Let cool slightly.
To make the panini, add spinach to one piece of bread. Add chicken cutlet, then top with pears. Add cheese over the pears, then spread fig jam on the top piece of bread and close the sandwich.
Spray a panini press with cooking spray and heat to high heat. Add the sandwich and press firmly. Cook until bread is golden brown and cheese has melted, about 5 minutes.