Remove the dough from the refrigerator. Divide into four equal pieces and form them into balls. Cover them with plastic and let them rest for 20 minutes.
On a floured surface, roll out each ball into a flat circle about 10 inches across. If it resists, let it rest for a minute and then continue rolling.
Place one of the circles on a sheet of parchment paper. Spread about a third of the jam on top. Place another circle on top of the first and spread with jam. Then the third circle and spread with jam. Then top with the fourth circle.
Place a glass, that is about 2 1/2 inces across, in the center of the circle. Cut all the way through the dough from the edge of the glass to the edge of the circle, dividing the dough into 16 equal sections with an uncut area in the center.
Remove the glass and select two sections that are side by side. Twist the two sections away from each other, twisting them two full rotations and then pinching them together at the tip. Continue around the rest of the circle until all of the sections are pinched together in this way.
Cover the dough with plastic wrap and allow it to rise in a warm place for about an hour and a half.
Preheat the oven to 350 degrees F. Wisk the egg with a Tablespoon of water, and brush it over the dough. Sprinkle the dough with the sugar. Cut the figs in half, removing the stems, and place them on each point of the star. Bake until golden brown, about 25 minutes to 30 minutes.
Remove the bread and parchment to a rack to cool.