In a re-sealable freezer bag, mix all ingredients for marinade and mix well. Place meat inside bag making sure it is well covered in marinade. Seal bag. Marinate meat in refrigerator for 2 hours.
Remove meat from bag and cook in a preheated pan or on barbecue over high heat for 15 to 20 minutes, turning over several times during cooking. Remove from heat and let stand for 10 minutes.
Slice meat into 5 mm (1/4 inch) thick slices.
In a bowl, mix mayonnaise and barbecue sauce.
Cut Panini in half and grill on barbecue. Spread BBQ mayonnaise sauce on bread and garnish with meat slices, lettuce, dill pickles and red onion.