Preheat Panini maker, grill pan, or skillet.
Trim and discard rind from Brie round and cut into slices about 1/4 inch thick.
Spread softened butter on one side of each piece of bread.
Spread Dijon mustard on the other side of bread.
Place one piece of bread, butter side down, on Panini maker.
Top with brie, turkey, and onions.
Place another bread slice on top and press down, cooking until golden brown.