Halve each mango and remove the pits. (To make it easier, I have cut the mangoes in quarters because it makes it easier to cut them away from the pit.) Remove the peels from each mango half. Cut diamond shapes about 1/2-inch deep in the top of the mango flesh, but be careful to not cut all the way through.
Place a medium saucepan on the grates of the grill (or on stove top over medium heat). Add the butter and brown sugar to the pan. Cook, stirring occasionally until the sugar has melted and the sauce thickens slightly, about 5 minutes.
Remove the pan from the heat and add the bourbon. Using a long match, ignite the bourbon and allow the flames to subside. Stir in the cinnamon, salt and chopped pecans.
Top mangoes with the sauce and garnish with a dollop of creme fraiche or sour cream, if using. (I usually skip the sour cream and just sprinkle a little extra chopped pecans).