In a medium saucepan over medium heat, combine fresh blueberries, white sugar, lemon juice, and lemon thyme. Stir occasionally as the mixture comes to a gentle boil. Allow it to simmer for about 20 minutes, until thickened and jammy, stirring occasionally. Once thickened, remove from heat and let the compote cool completely.

Take two slices of your hearty bread and spread a generous layer of the cooled blueberry compote on one side of each slice. Sprinkle a combination of white cheddar and mozzarella cheeses over the blueberry layer, ensuring even coverage for a gooey melt. Place the remaining slices of bread on top, pressing gently.

Heat a large skillet over medium-low heat and add a pat of unsalted butter, allowing it to melt and coat the pan. Carefully place two assembled sandwiches into the skillet and cook for 2-3 minutes, or until the bread reaches a golden brown color.

Once the first side is golden, gently flip the sandwiches using a spatula, adding a little more butter if necessary. Cook for another 2-3 minutes, ensuring both sides are evenly browned and the cheese is fully melted.

Carefully remove the sandwiches from the skillet and let them rest for a minute or two before slicing them in half. For an extra flavor boost, sprinkle a pinch of flaky sea salt and a few sprigs of fresh lemon thyme on top.