Preheat oven to 375 degrees with racks in the top and middle position. Place slices of baguette on a rimmed baking sheet. Toast on the middle rack until dry and light golden, 10 minutes.
Preheat broiler. Top each piece of baguette with 1 slice of Brie, 1 slice of persimmon, and a sprinkle of sugar (about ⅛ teaspoon each). Broil on top rack until sugar melts and cheese begins to bubble and turn golden, 1-2 minutes. Serve with cracked pepper.