In a medium saucepan, combine 1 cup of fresh blueberries, 1/4 cup of white sugar, 1 tablespoon of lemon juice, and a few sprigs of lemon thyme. Bring to a boil over medium-high heat, then reduce to low and simmer for about 20 minutes, stirring occasionally.

Remove from heat and let the blueberry compote cool down for around 10 minutes.

Spread a layer of blueberry compote on two slices of bread. Sprinkle shredded white cheddar and mozzarella over the compote, then top with remaining slices of bread.

Melt 2 tablespoons of butter in a large skillet over medium heat. Cook assembled sandwiches for 2-3 minutes until golden brown.

Flip the sandwiches, add remaining 2 tablespoons of butter, and cook for another 2-3 minutes until the other side is golden brown.

Remove from skillet and optionally sprinkle with flaky sea salt and fresh thyme before serving.