Heat a 12-inch nonstick skillet on medium-low heat.
Generously coat 1 side of each bread slice with mayonnaise. Place 2 bread slices, mayonnaise side down, into the skillet.
On 1 piece of bread, drizzle half the honey. Top with half of the arugula and then add half of the brie slices. On the other piece of bread add 2 slices of cheddar cheese and half of the apple slices. Cover the pan with a lid and let it cook until the bread starts to brown and the cheese starts to melt, about 3 minutes.
Once the cheese has started to melt, flip the brie half of the sandwich on top of the cheddar half. Cover the pan with the lid and let the sandwich cook for another 3 to 4 minutes, until the cheese is melted.