Prepare the Blackberry Balsamic Jam:

• In a small saucepan, combine the blackberries, sugar, balsamic vinegar, lemon juice, and a pinch of kosher salt.
• Bring the mixture to a boil over medium-high heat.
• Reduce the heat and let it simmer.
• Use a potato masher or wooden spoon to crush the berries as they cook.
• Continue simmering for 7 to 10 minutes until the mixture thickens into a jam-like consistency.
• Remove from heat and allow the jam to cool completely.

Assemble the Sandwiches:

• Spread butter on one side of each slice of sourdough bread.
• Place two slices, buttered side down, on a clean surface.
• Layer the Brie slices evenly on the unbuttered side of these bread slices.
• If using fresh thyme, sprinkle it over the Brie.
• Spread a generous amount of the cooled blackberry balsamic jam over the cheese.
• Top with the remaining bread slices, buttered side up.

Grill the Sandwiches:

• Heat a skillet over medium heat.
• Place the assembled sandwiches in the skillet.
• Cook until the bottom is golden brown, about 3 to 4 minutes.
• Carefully flip the sandwiches and cook the other side until golden brown and the Brie is melted, another 3 to 4 minutes.
• Remove from the skillet, let rest for a minute, then slice and serve warm.