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Prepare the Dough: Combine butter, brown sugar, baking soda, salt, cinnamon, honey, and orange zest in the bowl of a stand mixer fitted with a paddle attachment. Mix on low speed to moisten, then increase to medium and cream until light and fluffy, about 5 minutes. Add orange juice, then add the egg yolks one at a time and continue beating until smooth. Reduce the speed to low and sprinkle in the flour, mixing until well combined.
Knead the dough against the sides of the bowl to form a smooth ball. Flatten into a disc and wrap in plastic. Refrigerate until cool and firm but not hard, about 1 hour. (The dough can be refrigerated for up to 1 week; soften for 30 minutes at room temperature.)
Prepare the Preserves: Cut the figs in half. Pulse with applesauce and orange juice in a food processor until roughly chopped, then process to a thick, smooth paste. Scrape the bowl and blade with a flexible spatula, then process a minute more to ensure absolutely no chunks remain. Transfer to a sturdy piping bag fitted with a 1⁄2-inch plain tip and set aside until needed, up to 24 hours. (The preserves can be refrigerated in an airtight container for up to 3 weeks; bring to room temperature before using.)
To Assemble the Cookies: Adjust oven rack to middle position and preheat to 350°F (175°C). Knead the cool dough on a bare work surface until pliable and smooth, then dust with flour and roll into an 8-inch square. Sprinkle both sides with flour and roll into a 15-inch square. Slide an offset spatula under the dough to loosen it, brush off excess flour, and cut into four 3 1/4-inch strips.
Holding the bag at a 90-degree angle just above the surface of the dough (this will force the preserves to flatten as they leave the bag), pipe a 1-inch-wide strip down the center of each portion. Fold a long flap of dough over each strip, brush away excess flour, and roll each bar over, seam side down. Gently flatten each bar with your fingertips, then transfer to a parchment-lined half sheet pan (all four bars will fit on a single sheet).
Bake until the bars are puffed and firm, without any significant browning, about 18 minutes. Immediately cut into 1-inch pieces with a bench scraper, then transfer to an airtight container, with a paper towel between each layer and on top. This will steam the cookies and retain moisture for them to reabsorb, creating a uniquely soft and cakey texture. Cover and “mature” for at least 6 hours before serving; prior to that, the cookies will taste dry. Store for up to 1 week at room temperature or up to a month in the fridge.