Combine the blueberries, sugar, lemon juice, and bundled lemon thyme in a saucepan over medium-high heat.
Bring to a boil, reduce heat, and simmer for 10 minutes.
Lower heat to low and continue cooking for another 10 minutes, stirring often until thickened.
Remove the thyme bundle and let the jam cool for 10 minutes.
Spread the blueberry lemon thyme jam onto 4 slices of bread.
Top with shredded white cheddar and mozzarella cheese.
Place the remaining bread slices on top to form sandwiches.
Heat 2 tablespoons butter in a cast iron skillet over medium heat.
Cook two sandwiches for 2 to 3 minutes per side until golden and the cheese melts.
Repeat with remaining butter and sandwiches.
Cut in half and finish with flaky sea salt and fresh thyme if desired.
