In a medium saucepan, combine fresh blueberries, white sugar, lemon juice, and lemon thyme. Cook over medium heat until boiling, then simmer for 10-20 minutes until thickened.

Spread a layer of blueberry compote on one side of each slice of bread. Layer cheddar and mozzarella over the compote, and top with another slice of bread.

Heat a skillet over medium-low and melt butter. Ensure it bubbles without browning.

Cook the sandwiches for about 2-3 minutes on each side until golden brown and the cheese is melted.

Let the sandwiches sit for a minute before slicing in half to allow the compote to ooze slightly. Optionally, sprinkle with flaky sea salt and fresh thyme before serving.