In a medium saucepan, combine fresh blueberries, white sugar, lemon juice, and lemon thyme. Cook over medium heat until boiling, reduce heat, and let simmer for about 20 minutes until thickened. Remove from heat and cool completely.

Spread a layer of cooled blueberry compote on one side of two slices of bread. Sprinkle white cheddar and mozzarella cheese over the compote, then top with the other bread slices, pressing together gently.

In a skillet over medium heat, melt unsalted butter and place the sandwiches in the skillet. Cook for 2-3 minutes until golden brown, then flip and cover, cooking for another 2-3 minutes until cheese melts.

Remove from skillet, let cool slightly, slice in half, and garnish with flaky sea salt and additional lemon thyme. Serve with tomato soup if desired.