Preheat the oven to 180°C / 356°F.
Halve a sheet of phyllo pastry lengthwise.
Brush the top half of phyllo with melted butter and spread the butter between the layers, too.
Place the Brie in the middle of the folded phyllo sheet.
Wrap the first layer around the cheese as you would a gift.
Spoon the green fig jam on top of the cheese and sprinkle with fresh thyme.
Wrap the cheese in one more layer of buttered phyllo folded in half.
Fold the remaining sheet of phyllo twice and trim it into a 2-3 cm (1 inch) thick strip. Repeat to make the phyllo ribbons and the bow.
To shape the center of the bow, fold the phyllo sheet into a smaller strip - about 1.5 cm (1/2 inch) thick.
Arrange the ribbons and the bow, using the center piece to secure the bow (fold the ends of the strips to the back).
Brush with melted butter all over.
Bake the phyllo-wrapped Brie on a baking sheet for 22-25 minutes until golden brown and crisp.
Serve warm with crostini or baguette and extra jam.