Butter the outside pieces of the bread slices. Assemble the sandwiches by layering brie, peach slices, and basil. Drizzle with honey. Top each with remaining 4 bread slices, butter side up.
Using a grill pan or sandwich press, grill sandwiches for 2 minutes on each side or until lightly toasted and cheese melts. Remove from grill and cut sandwiches in half, if desired. Serve warm.
Note: You can also use a drizzle of balsamic vinegar instead of the honey.