Make the dough
Cream together the butter, sugar and zest in the bowl of a stand mixer fitted with the paddle attachment, for 2-3 minutes on medium speed. Scrape down the bowl and paddle.

Add the egg white and vanilla and beat in. Scrape down the bowl and paddle again.

Add the flour and beat on low speed until the dough comes together.

Wrap in plastic wrap and refrigerate for 2 hours or overnight.

Make the filling
Cut the figs in half and scoop out the seeds and pulp with a spoon. In a medium sauce pan, combine figs, sugar, and lemon juice. Mash mixture a few times with a potato masher or fork.

Cook mixture over medium-high heat until bubbling and sugar has dissolved; reduce heat to medium-low and simmer, stirring occasionally, for 30 minutes, until it has reduced by about one-third and is beginning to gel. Set aside until completely cool.

Assemble the Fig Newtons
Place racks in middle and lower third of the oven and preheat the oven to 350 degrees. Line baking sheets with parchment paper.

On a floured surface, roll the dough out to a 12 x 16 rectangle. Cut into 4 equal strips, each 12 x 4 inches. Spoon a line of filling down the center of each strip. Fold the dough over the filling and pinch the edges together. Using a serrated knife, slice each log on the diagonal into 10 cookies. Place each cookie on the parchment-lined baking sheets, seam side down.

Bake, rotating the baking sheets from top to bottom and front to back halfway through, for 12-15 minutes, until golden. Remove from the oven and allow to cool on a rack.