In a medium saucepan over medium-high heat, combine fresh blueberries, sugar, lemon juice, and bundled lemon thyme. Stir occasionally and bring to a boil, then reduce the heat and let it simmer gently for about 20 minutes.

Remove from heat when it coats the back of a spoon and let it cool while you prepare the sandwiches.

Lay out slices of bread. Generously spread the cooled blueberry compote on one side of half the bread slices.

Layer white cheddar and mozzarella cheese on top of the compote, then place the remaining bread slices on top.

Heat a non-stick skillet over medium heat and add butter. Once melted, place the sandwiches in the skillet.

Grill for 2-3 minutes until golden brown, then flip and grill the other side.

Remove from skillet, let rest for a minute, then slice in half. Sprinkle with flaky sea salt and garnish with fresh thyme.