How to make cake like cookies crispy
In general, to create crispier cookies:


baking soda (if you use this to replace the baking powder, keep in mind it's thought to be 3x as strong, so reduce accordingly. The decrease in acid leads to a longer set temp, which will help your cookie bake to be crispier. If you'd like to even out the decrease in acid, you can always use a little bit of each, or even add in a little lemon juice)
replace the egg (with whole milk to encourage spreading)
make sure the butter you're creaming is at the right temperature (read this post for more info: http://blog.kingarthurflour.com/2015/04/27/creaming-butter-sugar/)
bake it for longer at a lower temp with smaller flatter cookies


All of these tips are meant to increase the surface area of the cookie exposed to the heat, in order to dry it out/crisp it up. However, your cookie recipe also has the addition of all the water and stickiness of the fruits, so it is unlikely that you can get it to be completely dry and crispy, like a sugar cookie, for instance.

Tips gathered from many sources and experience, but the best one for cookies found was this one: http://blog.kingarthurflour.com/2015/04/27/creaming-butter-sugar/

Good luck on our quest for crispier fig cookies!