In the bowl of a food processor, combine the 3/4 cup [135 g] of the figs and the granulated sugar. Pulse until the figs and sugar are combined and the mixture resembles coarse sand, about 10 pulses.
In the bowl of a stand mixer fitted with a paddle, beat the butter on medium speed until creamy, about 1 minute. Add the granulated sugar and fig mixture, orange zest, and salt, and beat again on medium speed until light and fluffy, 2 to 3 minutes. Scrape down the bowl and add the egg yolk and vanilla, and mix on low speed until incorporated.
Add the flour and mix on low speed until just combined. Add the candied orange peel and chopped figs, and mix until combined.
Transfer the dough to a workspace and form the dough into a 12 in [30.5 cm] long log. Place the log on a large piece of plastic, a few inches longer than the log. Sprinkle the sanding sugar over each side of the log, covering the outside of the dough. Gently press the sugar into the dough with your hands. Wrap the log in the plastic wrap and refrigerate until firm, about 4 hours.
Adjust an oven rack to the middle of the oven. Preheat the oven to 350°F [180°C]. Line three sheet pans with parchment paper.
Slice the chilled log into ¼ in [6 mm] thick rounds. Space the rounds about 2 in [5 cm] apart on the sheet pans.
Bake one pan at a time, rotating halfway through baking. Bake until the edges are very light golden brown but the centers are still pale, 14 to 16 minutes.
Transfer the pan to a wire rack and let the cookies cool completely on the pan. Store cookies in an airtight container at room temperature for up to 4 days.