Preheat the oven to 350 degrees.
Place a piece of parchment on your work surface and dust with a liberal amount of flour. Roll the dough into a rectangle that's about 11 inches long by 13 inches wide, and ¼ inch thick. Trim the edges so that you have a clean rectangle shape. Then, use a ruler to cut strips that are 3½ inches wide.
Add the fig filling to a pastry bag or a ziplock bag, and cut off about ½ inch of the tip. Pipe the fig filling down the center of each strip of dough. The filling will be about 1 inch wide and ½ inch thick.
Fold one of the long sides of dough up and over the filling, brush with egg wash, then fold the other long side of dough up and over the filling, making sure to overlap the edges about ¼ of an inch. Press the long seam gently with your fingers to seal and gently lift each log onto a parchment covered baking sheet. Press the ends to seal those too.
Chill or freeze for at least 10 minutes, to firm the dough. Use a sharp knife to trim each bar into several 1" long cookies. Chill again, for 10 minutes.
Turn cookies over, seam-side down, and brush with egg wash.
Bake for 13-15 minutes, until the dough is set and slightly firm to the touch. Remove from the oven and let cool on the baking sheet for 1 minute. Transfer to a cooling rack and cool completely.
Store Homemade Fig Newtons in an airtight container at room temperature for up to 1 week.