Preheat a skillet or pan over medium heat.
In a small bowl, mix the mayonnaise and Dijon mustard together until well combined.
Spread the mayonnaise mixture evenly on one side of each slice of bread.
On the unspread side of one slice, layer the sliced Brie cheese, turkey breast, cranberry sauce, and arugula or spinach if using.
Top with the second slice of bread, spread side facing out.
Spread the softened butter on the outside of both slices of bread.
Place the sandwich in the preheated skillet and cook for about 3-4 minutes on each side, or until the bread is golden brown and the cheese is melted.
Remove from the skillet, slice in half, and serve warm.