In a small saucepan, combine blueberries with sugar over medium heat. Stir gently and cook for 5–7 minutes until the blueberries burst and the mixture becomes jammy. Remove from heat to cool slightly.

Spread cream cheese or brie on one side of each slice of bread. Sprinkle shredded mozzarella or fontina cheese over the cream cheese on two slices, then spoon the warm blueberry mixture on top. Top with the remaining bread slices, cream cheese side down.

Preheat a skillet over medium-low heat. Butter the outer sides of each sandwich. Once the skillet is hot, place the sandwiches in and cook undisturbed for about 3–4 minutes until golden brown.

Carefully flip the sandwiches and cook for another 3–4 minutes, watching for golden color. Cover briefly to achieve a gooey interior.

Once both sides are golden brown and the cheese is melted, transfer to a cutting board to rest for 1–2 minutes. Slice diagonally and sprinkle with flaky sea salt.