Combine the fresh blueberries, white sugar, lemon juice, and bundled lemon thyme in a 2-quart saucepan over medium-high heat. Bring the mixture to a boil, then reduce the heat to medium-low and simmer for 10 minutes.

Lower the heat to low and continue simmering for another 10 minutes (20 minutes total), stirring often until the jam thickens and coats the back of your spoon. Remove and discard the lemon thyme bundle. Allow the jam to cool to room temperature, at least 10 minutes.

Lay out 4 slices of bread. Spread about 2 tablespoons of the cooled blueberry lemon thyme jam evenly onto each slice. Sprinkle the white cheddar and mozzarella cheeses over the jam. Top with the remaining 4 bread slices to form sandwiches.

Heat a 12-inch cast iron skillet over medium to medium-low heat and add 2 tablespoons of butter, letting it melt and coat the pan.

Place two assembled sandwiches in the skillet and cover with a lid. The lid traps steam to help melt the cheese. Cook for 2 to 3 minutes until golden on the bottom.

Flip the sandwiches and cook for another 2 to 3 minutes, or until the bread is golden and the cheese is melted. If bread browns too quickly, lower the heat.

Transfer the cooked sandwiches to a cutting board, add the remaining 2 tablespoons of butter to the skillet, and repeat with the remaining two sandwiches.

Cut each sandwich in half. Top with a sprinkle of flaky sea salt and extra lemon thyme leaves if desired.