Preheat your oven to 350°F and position a rack in the middle. While the oven heats, measure out all your ingredients and chop the almonds into fine, uniform pieces (about 1/8-inch)—this ensures even coating and consistent texture on the cookies. Having everything ready before you start mixing is key to a smooth, stress-free baking process.
In a mixing bowl, beat the room-temperature butter with brown sugar for 2-3 minutes until the mixture is light, fluffy, and pale. This creaming process incorporates air into the dough, which creates a tender, delicate cookie texture. Don't skip this step—proper creaming makes a real difference in the final result.
Add the egg yolk and almond extract to the creamed mixture from Step 2 and beat for 1 minute until fully incorporated. Then add the flour and salt, mixing on low speed just until the dough comes together—don't overmix, as this can develop too much gluten and make the cookies tough. Once combined, transfer the dough to the refrigerator for 15 minutes to firm up, which makes shaping much easier.
While the dough chills, whisk the egg white in one small bowl until foamy (about 30 seconds), and mix the chopped almonds with the raw coarse sugar in another bowl. Remove the chilled dough from the fridge and roll it into 12 equal balls—I find rolling between my palms gives a smooth, even sphere. Dip each dough ball into the egg white, then immediately roll it in the almond-sugar mixture, coating all sides evenly.
Place the coated dough balls on a parchment-lined baking sheet, spacing them about 2 inches apart. Using your thumb or the back of a small spoon, press a gentle indent into the center of each cookie—don't press too hard or you'll crack the almond coating. Bake for 8 minutes until the cookies are just set but still pale; they should look slightly underdone at this point.
Remove the cookies from the oven and while they're still warm, spoon about 1 teaspoon of fig spread into the center indent of each cookie. Return the baking sheet to the oven and bake for 7-8 minutes more until the edges are golden brown and the fig spread is warm. The cookies will continue to set as they cool, so don't overbake or they'll become dry.
Remove the cookies from the oven and let them cool on the baking sheet for 5 minutes—this helps them firm up without cracking. Transfer to a wire rack to cool completely before serving. Store in an airtight container for up to 5 days.