Stir cocoa with whisk into sugar before adding water and lemon.
Combine figs, sugar cocoa mixture, water, and lemon juice in a medium saucepan and bring to a boil.
Reduce heat and simmer until the liquid has thickened slightly and has turned a rosy, golden shade, about 6-8 minutes.
Turn off the heat. Stir in vanilla bean paste and cool the mixture for 10 minutes.
Transfer to a food processor and puree until smooth.
Store in an airtight container (like a mason jar) in the refrigerator for up to a week.
For the cookies:
Preheat oven to 350°F. Line baking sheets with parchment paper.
Sift flour, cocoa, and salt into a small bowl.
Cream butter and sugar with an electric mixer on medium-high speed until fluffy.
Reduce speed to medium and add the egg yolks, cream, and vanilla extract. Scrape the sides of the bowl. Add the flour mixture and beat until just combined.
Roll ball using 2 tsp dough for each. Roll the balls into the sugar in the bowl.
Place 1 inch apart. With a wine bottle cork (or the handle of a wooden spoon), press gently in the center of each ball to create an indentation.
Bake, rotating sheets half way through, until cookies are set, about 10 minutes.
Let cool slightly on baking sheets, then transfer to wire rack to cool.
Using a spoon, or pastry bag, place a dollop of the Cocoa Fig Jam into the indent of the cookies.
