Spread fig jam on 2 slices of bread. Top with cheese, arugula and remaining slices of bread. Brush each sandwich lightly with olive oil on both sides.
Place a cast-iron or nonstick skillet over medium heat. Add sandwiches and press down slightly with a spatula. Cover and cook until golden brown on one side, 3 to 4 minutes. Flip and cook until second side is golden brown, 3 to 4 minutes. Serve warm.