Flip the bread slices (butterless sides up), spread apricot jam on one slice and brie on the other. Cut off the rind of the brie if you wish. Remove the thyme leaves from the twig by gently pulling downward from the top of the sprig and sprinkle over the cheese.
Put the slices together and place the sandwich in the pan. Cook for about 3 minutes per side, taking care not to burn the bread. Once the bread is toasted + golden and the cheese is melted, remove from the pan and serve immediately.