In a small saucepan, combine the blackberries, sugar, balsamic vinegar, lemon juice, and kosher salt.

Bring to a boil over medium-high heat, then reduce heat and simmer. Crush the berries with a wooden spoon or potato masher to help them break down.

Simmer the jam for 7 to 10 minutes until it thickens. Transfer to a small bowl and set aside to cool completely.

Slice the brie cheese into 1/4 inch thick slices and heat a large skillet over medium heat.

Spread butter on one side of four bread slices and place them butter-side down in the skillet.

Top the bread with brie slices and fry slowly until the bread is golden and the cheese begins to soften.

Sprinkle the chopped thyme over the cheese. Spread a thick layer of blackberry jam on the remaining bread slices and place them jam-side down over the brie.

Butter the top side of the bread, flip the sandwiches carefully, and continue to fry until the bottom is golden brown and the brie is fully melted.

Transfer to a cutting board and let cool for 2 minutes before slicing with a sharp knife.