In a medium saucepan, combine fresh blueberries, sugar, lemon juice, and a bundle of lemon thyme over medium-low heat. Bring to a gentle boil, then reduce heat and simmer for about 20 minutes until thickened. Stir occasionally and remove thyme once glossy. Allow to cool.

Spread a generous layer of cooled blueberry compote on one side of each slice of thick bread. Top with a mixture of white cheddar and mozzarella cheese and close the sandwiches.

Heat a cast iron skillet over medium heat and add unsalted butter. Once melted, add the sandwiches and cook for 2-3 minutes on one side until golden brown. Flip and cook for another 2-3 minutes until cheese melts.

Remove sandwiches, let cool briefly, sprinkle with flaky sea salt and fresh thyme if desired, cut in half, and serve warm.