Preheat your oven to 325°F (165°C).
Prepare the brie cheese by trimming the top rind and place it on a parchment-lined baking sheet; set aside.
To make the blackberry sauce – In a saucepan, combine blackberries, sugar, water, salt, and balsamic vinegar. Mash gently to break up the berries, then cook over medium-high heat until the sauce reduces and thickens (approximately 5-7 minutes). Remove from heat, add the basil leaves to infuse for 10 minutes, then discard the basil.
To toast the pecans – In a skillet, toast the chopped pecans over medium-high heat, stirring frequently. When they become fragrant, add sugar, salt, and butter. Stir until the sugar melts and coats the pecans. Remove from heat and transfer to a plate to cool.
To assemble, spoon the blackberry sauce over the brie, then sprinkle with toasted pecans. Place in the oven to warm the brie until softened, about 5-7 minutes.
Serve warm with crackers or sliced baguette.