Combine blueberries, sugar, lemon juice, and tied lemon thyme in a 2-quart saucepan over medium-high heat. Bring to a boil, then reduce to medium-low and simmer for 10 minutes. Lower heat and cook 10 more minutes until thickened. Remove thyme and let cool.

Lay out 4 bread slices and spread with cooled blueberry jam. Top with mixed white cheddar and mozzarella cheeses. Close with remaining bread slices.

Heat cast iron skillet over medium heat. Add 2 tablespoons butter and melt. Cook two sandwiches covered for 2-3 minutes per side until golden and cheese melts. Adjust heat as needed to prevent burning.

Repeat with remaining butter and sandwiches.

Cut sandwiches in half. Sprinkle with flaky sea salt and extra lemon thyme leaves if desired.