In a medium saucepan, combine fresh blackberries, balsamic vinegar, sugar, lemon juice, and kosher salt. Bring to a boil, then reduce heat and simmer for 7-10 minutes, crushing the blackberries until a thick jam forms. Remove from heat and let cool.

While the jam cools, slice the brie into ½ inch thick pieces. Heat a skillet over medium heat.

Butter one side of four slices of sourdough. Place in the skillet, buttered side down, layer brie, and grill for 3-4 minutes until golden and cheese softens. Sprinkle with thyme.

Spread blackberry jam on the unbuttered side of remaining bread. Place jam-side down on brie. Butter the tops and grill the other side for another 3-4 minutes until crispy.

Let cool for a minute before cutting in half. Serve warm.