Place sliced strawberries in a small bowl and drizzle with balsamic vinegar. Set aside.
Place the sourdough on a flat surface and spread the mayonnaise on the outside pieces.
Flip the bread over and top one slice with goat cheese, the strawberries, basil and then the brie. Close the sandwich with the other slice.
Heat a skillet over medium-low heat.
Place the sandwich on the skillet and grill until golden brown on one side, about three minutes. Flip and grill the other side until browned and crispy. Reduce the heat if needed to allow the bread to get crispy, without burning and the cheese to melt.