In a medium saucepan over medium heat, combine fresh blueberries, white sugar, lemon juice, and thyme. Stir gently as it comes to a boil, then reduce heat and simmer for about 10 minutes.

Once the blueberry compote reaches a thick, spreadable consistency, remove it from the heat. Allow it to cool for about 10 minutes.

Take two slices of hearty bread and spread a generous layer of cooled blueberry compote on one side of each slice. Add white cheddar and mozzarella cheese on top, then place another slice of bread on top.

Evenly coat the outer sides of each sandwich with butter to achieve a golden-brown crust.

Heat a non-stick skillet over medium heat. Place the sandwiches in the skillet and grill each side for about 2-3 minutes until golden brown and cheese begins to melt.

Once done, let the sandwiches cool slightly, slice in half, sprinkle with flaky sea salt, and serve immediately.