In a medium saucepan, combine fresh blueberries, white sugar, lemon juice, and optional lemon thyme. Cook over medium-high heat, stirring gently until the mixture reaches a boil. Once bubbling, reduce the heat to low and let it simmer for about 15-20 minutes, stirring occasionally, until the compote thickens and becomes syrupy. You'll know it's ready when the blueberries have burst and the sauce clings to the back of a spoon.

Once the blueberry compote has cooled, spread a generous layer of the compote on one side of four slices of hearty bread. Pile on slices of white cheddar and whole milk mozzarella cheese. Top with the remaining slices of bread, compote side down.

In a large skillet, melt a tablespoon of butter over medium heat. Place the assembled sandwiches in the skillet. Cook for about 2-3 minutes, or until the bottom is golden brown and crispy. Flip the sandwiches, adding another tablespoon of butter if needed, then cover the skillet to melt the cheese completely.

Remove the sandwiches from the skillet and let them rest for a minute before slicing in half. Optionally, sprinkle with flaky sea salt and fresh thyme before serving.