Make the Blackberry Balsamic Jam:

1. Combine Ingredients: In a saucepan over medium-high heat, combine the fresh blackberries, balsamic vinegar, sugar, lemon juice, and a pinch of kosher salt.
2. Cook the Jam: Bring the mixture to a boil, then reduce the heat to a simmer. Mash the blackberries with a wooden spoon or potato masher to break them down.
3. Simmer: Let the jam simmer for 7-10 minutes, stirring occasionally, until it thickens to a jam-like consistency.
4. Cool the Jam: Transfer the jam to a bowl and allow it to cool to room temperature.

Prepare the Sandwiches:

1. Slice the Brie: Cut the double cream brie into ½-inch thick slices.
2. Toast the Bread: Heat a skillet over medium heat. Butter one side of four slices of sourdough bread and place them buttered-side down in the skillet.
3. Add the Brie and Thyme: Top each slice of bread with brie slices and a sprinkle of chopped thyme. Cook until the bread is golden and the brie begins to soften.

Assemble the Grilled Cheese:

1. Spread the Jam: Spread a generous layer of the blackberry balsamic jam on the unbuttered side of the remaining four slices of bread.
2. Assemble the Sandwiches: Place each jam-covered slice on top of the brie-topped slices, jam side down.
3. Butter the Top: Butter the top of each sandwich.
4. Flip and Cook: Carefully flip the sandwiches and cook until the cheese is melted, and both sides are golden brown.

Serve:

1. Let Cool Slightly: Transfer the sandwiches to a cutting board and let them cool slightly.
2. Slice and Serve: Slice the sandwiches in half and serve warm.

Pro Tip:
For an extra layer of flavor, drizzle a little honey on top of the grilled cheese or add extra thyme.