Preheat the oven to 350°F. Using the beater attachment, beat together the butter and sugar in the bowl of a stand mixer. Add the egg yolk and vanilla extract and mix until combined.
Whisk together the flour and baking powder and incorporate into the butter/sugar mixture.
Remove the dough, taking a little piece at a time, and form it into cookies. Place the cookies on a greased baking sheet and use your thumb to create an indentation in the middle of each one.
Fill each cookie with a dollop of fig jam and bake at 350°F for 15 minutes.