Prepare Blueberry Compote: In a saucepan, combine fresh blueberries, white sugar, lemon juice, and lemon thyme. Bring to a boil, then reduce the heat and simmer for 20 minutes until it thickens, stirring occasionally.

Assemble Sandwiches: Once your blueberry compote is cool, spread it generously on four slices of your chosen bread. Pile on the shredded white cheddar and mozzarella cheese, then top with the remaining bread slices.

Grill Sandwiches: Heat a skillet over medium heat and add a layer of butter. Place the assembled sandwiches in the skillet and grill for 2-3 minutes on each side until golden and the cheese is perfectly melted. Adjust the heat to prevent burning.

Serve: Slice the sandwiches in half for easy sharing and enjoyment. For a touch of elegance, sprinkle with flaky sea salt and garnish with fresh thyme if desired.