Cut the loaf of bread lengthwise into six long, oval slices, each between ¼ and ½ inch thick. Spread one side of three slices with the fig jam. Spread the mustard on the other three slices; then layer the cheese over the mustard.
Coat a medium nonstick skillet with cooking spray and warm it over medium heat. Add the onion, salt, and pepper. Cover the skillet and cook the onion until it is very tender, 6 to 8 minutes, stirring now and then. Stir in the thyme.
Arrange the onion over the cheese; then layer on the ham. Top with the jam-spread slices of bread. Coat the sandwiches all over with cooking spray.
Warm a grill pan or panini press to medium-high heat. Place the sandwiches, in separate batches if necessary, on the hot grill pan and compress them slightly with a heavy weight, such as a cast-iron pan or foil-wrapped brick. If using a panini press, push the lid down on the sandwiches. Cook them until nicely browned and the cheese melts, 3 to 5 minutes per side on the grill pan and 6 to 8 minutes without turning in the panini press. Cut each sandwich in half on a diagonal and serve hot.
Tip: If the Panera Bread Three Cheese Loaf isn’t available, you can use a loaf of Panera Bread Asiago Cheese, Sourdough, Honey Wheat, or All-Natural White Bread.