Separate bagels and add butter to one side. Set aside.
Slice brie cheese. I lay the wheel down so it is flat and cut 6 pieces. The pieces should be about an inch wide. Trim off the rind.
If using a skillet, set heat to medium high. Lay one side of bagel thin on grill/skillet. Add one slice of white cheddar cheese, a thin layer of fig preserves (so it is coated, but not overflowing), three pieces of brie and the second slice of white cheddar. Top with bagel thin top. Repeat with other sandwich.
Close George Foreman grill and cook for 4-5 minutes. Sandwich is done when cheese is melted. If using a skillet, heat 4-5 minutes on one side and flip. Cook for 4-5 more minutes.
Lift one bagel thin top and had a small handful of arugula; repeat on other side.