Special equipment: kitchen string
Preheat the oven to 180 degrees C (350 degrees F) and grease a baking tray with some butter.
Add 1 tablespoon of butter to a medium-sized saucepan over medium heat, and when it starts to foam add the sugar, balsamic vinegar, thyme and figs. Simmer gently until the figs have softened and start to become sticky, about 10 minutes, or. Turn down the heat if the figs start to burn, and add the the water or orange juice for extra liquid if required. Set aside.
Meanwhile, melt the remaining 4 tablespoons of butter. Lay out 1 sheet of phyllo pastry at a time and brush with some of the melted butter. Keep the remaining sheets covered with a damp, clean dishcloth as you work; this prevents them from drying out. Once you have brushed 1 sheet, lay the next sheet over the buttered one, brush with melted butter, and repeat until you have used all f sheets. Turn the stack of sheets over and brush the underside with melted butter too.
Place the Brie in the center of the pastry stack, spoon over the fig jam, gather the corners of the phyllo together and twist at the top. Secure with kitchen string if necessary. Gently place the pastry package onto the baking tray and bake until the pastry is golden, 20 to 25 minutes. Serve warm with fresh bread or crunchy crostini.