Preheat the oven to 400 degrees.
In a bowl, add balsamic vinegar, strawberries, pepper, and thyme. Mix vigorously, cover with plastic wrap, and allow to sit in the refrigerator for 10 minutes (up to an hour).
With your hands, flatten the baguette out so that it is as thin as possible.
Butter the inside of the baguette and invert it. The outer crust is now going to be the inside of the sandwich.
Assemble sandwiches by placing some sliced Brie onto the outer crust of the baguette, buttered sides facing out.
In a large pan over medium heat, cook the sandwiches using a weight (another pan, or a brick wrapped in foil) to press down on the sandwich lightly.
Flip and repeat so both sides are nicely browned.
Allow sandwiches to rest for 3 minutes before slicing and eating.