In a medium saucepan over medium heat, combine 2 cups of fresh blueberries, 1/3 cup of sugar, the juice of 1 lemon, and a few sprigs of lemon thyme. Bring to a boil, stirring occasionally; then reduce heat and simmer gently for about 20 minutes until thickened.

Take four slices of sturdy bread and spread a layer of cooled blueberry compote on two of the slices. Top with thick slices of white cheddar and mozzarella cheese, then cover with the remaining slices to create sandwiches.

Preheat a cast-iron skillet over medium heat and add 2 tablespoons of unsalted butter. Once melted, place the assembled sandwiches in the skillet. Cover and cook for 2-3 minutes until golden-brown and cheese starts to melt.

Carefully flip each sandwich using a spatula, adding more butter if necessary. Cover again and cook for another 2-3 minutes until crispy and golden. Check for desired doneness.

Transfer the sandwiches to a cutting board, cut in half to reveal the melted cheese and blueberry compote. Optionally, sprinkle with flaky sea salt and garnish with thyme leaves. Enjoy warm!