In a medium saucepan over medium heat, combine fresh blueberries, sugar, lemon juice, and lemon thyme. Stir and bring to a boil, then reduce heat to low and simmer for about 20 minutes. Remove from heat and let cool.

Lay out four slices of your chosen bread on a clean surface, ensuring even thickness for balanced crunch when grilled.

Spread a layer of cooled blueberry compote on two slices of bread, add white cheddar cheese and mozzarella cheese, then top with another slice of bread to create two sandwiches.

In a skillet over medium-low heat, add butter and let it melt. Place the sandwiches in the skillet and cover. Grill for about 2-3 minutes until golden brown.

Flip each sandwich gently using a spatula, add more butter if needed, cover and grill for another 2-3 minutes until the other side is browned and cheese is melted.

Transfer the grilled sandwiches to a cutting board, let cool for a minute, and cut them into halves or triangles. Optionally sprinkle with flaky sea salt.