Whisk the flour, baking powder, and salt together in a mixing bowl. Set aside.
Beat the butter and brown sugar in a large bowl (or the bowl of a stand mixer fitted with the paddle attachment) until light and fluffy, about 3 to 5 minutes.
Add the egg, vanilla, and orange zest and beat until combined. Stir the flour mixture into the butter mixture until well blended. The dough will be very soft. Scoop it out onto a piece of plastic wrap, shape into a disc, and refrigerate for at least 4 hours or overnight.
Meanwhile, make the filling. Combine the figs and water in a medium saucepan. Bring the water to a boil, cover, and allow the water to boil until the figs have absorbed it. If your figs are very dry and tough, you may need to use more water and simmer longer to get the figs to soften.
Transfer the figs to a food processor and pulse, scraping down the bowl occasionally, until the mixture is completely smooth. Allow the filling to cool.
Preheat the oven to 325 F. Place a large piece of parchment on your work surface and flour it liberally. The dough is very soft. Divide the chilled dough into 4 pieces. Place one piece of dough on the parchment and return the others to the refrigerator.
Shape the piece of dough into a rectangle by squaring it on the work surface (tap the 4 sides on the surface until they form a rectangle). Roll the dough, stopping frequently to make sure it is not sticking to the parchment, into a long rectangle, about 4 inches wide by 12 inches long. Be vigilant about lifting up the dough and re-flouring it to prevent sticking.
Scoop the fig filling into a pastry bag or a plastic zip-top bag with one corner cut off. Pipe the filling in a 1-inch strip down the center of the dough rectangle. You may need to flatten the filling a bit – it's easier to do this if you dip your fingers into some water first.
Fold one side of the dough over the filling, then the other. Press down on the seam to close it. Using the parchment, flip the cookie roll over, seam-side down. Brush any excess flour off the parchment and transfer it gingerly to a baking sheet and refrigerate while you repeat this step with the other 3 pieces of dough.
Bake for about 16 minutes or until the dough is no longer tacky and has begun to brown around the edges.
While the cookie rolls are still warm, either transfer them to a cutting board (a large spatula helps) or cut them directly on the baking sheet. Cut into 1 1/2- to 2-inch cookies. You may need to wipe off your knife every so often – the filling is rather sticky at this point.
Immediately place the cookies in a single layer inside a plastic zip-top bag and close the bag. In order to keep the cookies soft, they need to steam. Cool the cookies completely. Remove them from the bags and place in an airtight container. They can be kept, at room temperature, for up to 2 weeks.