Slightly pre-toast bread slices either on a skillet or toaster oven. Remove.
Spread mustard on one slices of bread then layer on slices of prosciutto, slices of persimmon, and a small handful of arugula onto two slices. Spread Brie cheese onto the other bread pieces. Sandwich the two parts together.
Heat butter in a medium skillet over medium heat. Place sandwiches in the pan, Brie side down, and grill until cheese is melted and bread is toasted to a golden brown. Flip sandwiches and cook until golden.