In a saucepan, combine the blackberries, balsamic vinegar, sugar, lemon juice, and a pinch of kosher salt. Bring to a boil over medium-high heat. Then, reduce the heat and let it simmer, crushing the berries with a wooden spoon until it thickens into a jam, about 7-10 minutes. Set aside to cool.

Slice the brie cheese into ½ inch thick slices. Heat a skillet over medium heat. Butter one side of four slices of sourdough bread and place them butter side down in the pan. Top with slices of brie and let it melt slowly until the bread is golden brown. Sprinkle with chopped thyme for added flavor.

Spread a layer of the homemade blackberry jam on the remaining bread slices and place them jam side down over the brie. Butter the top side and carefully flip the sandwich. Fry until the bottom bread is golden brown and the brie is melted, which should take about 3-4 minutes.

Transfer the sandwiches to a cutting board, let them cool for a couple of minutes, then cut in half with a sharp knife. Enjoy this delicious creation!