In small skillet, heat oil over medium-high heat; sauté onions for 5 to 7 minutes or until tender and lightly golden. Spread 1/2 tsp mustard on each of 4 bread slices. Layer onion slices, one slice of cheese, chicken, apple slices and remaining slice of cheese over top; cap with remaining bread. Lightly butter sandwiches on the outside. Preheat panini press according to manufacturer’s instructions; grill sandwiches for 2 to 3 minutes per side or until toasted and well marked. To serve, cut in half.
Tip: Use sweet onion instead of red onion if you prefer a sweeter and milder onion flavor.