Make the honey butter by whisking the butter and honey until smooth. Reserve.
Heat your panini press (or a grill pan or skillet).
Spread the butter on one side of each slice of bread. Then, layer the brie on top of the butter followed by apple slices. Top one side of each sandwich with arugula.
Fold the sandwiches together.
Add sandwiches to panini maker and press for about 10 minutes or until the cheese is melted. If you don't have a panini press, you can make these easy sandwiches in a nonstick skillet or grill pan, much like you make grilled cheese sandwiches. Place another heavy pan on top of the sandwich while cooking if desired to get a panini press effect.
Serve apple arugula brie panini with cheese and crackers, and riesling.