In a small bowl, combine the mashed blackberries, peach slices, honey, and thyme. Let sit for 5 minutes while you prep everything else. This helps the fruit soften slightly and the flavors meld.

Spread goat cheese on two slices of bread. Layer brie on top, then divide the blackberry-peach mixture between the sandwiches, letting some excess juice drain off first. Top with remaining bread slices. Butter the outside of each sandwich generously - this is what gives you that shatteringly crisp crust.

Heat a large nonstick skillet over medium-low heat. Place sandwiches butter-side down and cook for 3-4 minutes until deep golden brown and crisp. Press gently with a spatula to help everything adhere. Flip carefully and cook another 3-4 minutes until the second side is equally golden and the cheese is fully melted. If the bread is browning too fast before the cheese melts, lower the heat and cover the pan briefly.

Transfer to a cutting board and let rest for 1 minute - this keeps the filling from squishing out when you cut. Slice in half diagonally, sprinkle with flaky sea salt, and serve immediately while the cheese is still molten.