In a saucepan over medium-high heat, combine fresh blueberries, sugar, lemon juice, and lemon thyme. Bring to a boil, then simmer for about 20 minutes until thickened. Remove thyme and cool slightly.

Lay out four slices of bread. Spread cooled blueberry compote on each slice. Sprinkle white cheddar and mozzarella over compote, then top with remaining bread slices.

Heat a cast-iron skillet over medium heat and melt the butter. Place sandwiches in skillet, cover, and cook for 2-3 minutes until golden brown.

Flip sandwiches and cook for another 2-3 minutes until cheese melts and the other side is golden. Sprinkle with sea salt and fresh thyme if desired, cut in half, and serve hot.