Combine the chopped figs and water in a small pot and bring to a boil over medium-high heat. Once boiling, reduce the heat to low and simmer until the water is completely absorbed and the figs become very soft, about 8-10 minutes. Transfer the cooked figs to a blender and puree until completely smooth with no chunks remaining. Set the fig filling aside to cool to room temperature—this takes about 15-20 minutes and can happen while you prepare the dough.

Preheat your oven to 350°F while you prepare the dough. In a large mixing bowl, beat the softened butter and sugar together on medium-high speed for 3 minutes until the mixture is pale, fluffy, and significantly increased in volume. This creaming process incorporates air into the dough, which helps create a tender cookie texture. Make sure your butter is truly softened to room temperature—cold butter won't cream properly and will make mixing difficult.

Add the room-temperature egg yolks, vanilla extract, and orange zest to the creamed butter mixture and beat on medium speed for about 1 minute until fully combined and smooth. In a separate small bowl, whisk together the flour and salt. Add the dry ingredient mixture to the wet ingredients and mix on low speed just until the dough comes together—don't overmix or the cookies will be tough. The dough should be soft but still hold its shape when rolled.

Roll the dough into 1-inch balls using your hands or a small cookie scoop and arrange them on a parchment-lined baking sheet, spacing them about 1.5 inches apart. Using your thumb or the back of a small spoon, gently press a well into the center of each dough ball, being careful not to press through to the bottom. Bake for 8-10 minutes until the cookies are just set but still pale—they should not be browned yet. Remove from the oven and let cool on the sheet for 2-3 minutes.

While the cookies are still warm and slightly soft, gently re-press the wells with your thumb if they've puffed up during baking. Spoon about 1/2 teaspoon of the cooled fig filling from Step 1 into each well, pressing it down gently so it stays in place. Return the baking sheet to the oven and bake for 3-4 minutes more until the edges of the cookies turn golden brown. I like to fill the cookies while they're still warm because the gentle heat helps the fig filling settle nicely into each well.

Remove the cookies from the oven and let them cool on the baking sheet for 5 minutes to set up slightly, then transfer them to a wire cooling rack to cool completely. This two-stage cooling prevents the delicate cookies from breaking apart while still allowing them to firm up properly. Once completely cooled, the cookies can be stored in an airtight container for up to 5 days.