Combine all marinade ingredients and add to a resealable plastic bag.
Add mushrooms and onions and marinate for 2 to 3 hours.
Spray your grill pan or panini maker with nonstick cooking spray (you can use butter too).
Add cheese to bottom of sandwich bread, and top with mushrooms and onions. Close sandwich, place in panini maker, and grill for 5 to 6 minutes.
If using a grill pan, cook 3 to 4 minutes on each side.