In a small saucepan, stir together the honey, balsamic vinegar and thyme and set it over low heat. When it comes to a bubble, let it simmer for about 1-2 minutes, then drop in the berries and let it warm in the juices for another minute. Remove from heat and set aside. Discard the thyme.
While the balsamic berries cools and thickens, toast the bread. Slice the burrata cheese into 4 pieces, about 1 oz apiece. Place the burrata on the toasted bread, season lightly with salt, and top with the balsamic berries. Enjoy immediately.