Place the softened butter and brown sugar in a stand mixer fit with the paddle attachment. Beat on medium high speed until fluffy, about 2 minutes.
Scrape down the sides of the bowl and add the egg and vanilla extract. Mix until combined.
Scrape down the bowl and add the cocoa powder, espresso powder, flour, baking soda and salt. Mix on low speed, gradually increasing to medium. Mix until just combined and no streaks of flour remain.
Crumble the halva into your cookie dough and use a rubber spatula to fold the dough a few times to distribute the halva throughout.
Use a 2 ounce cookie scoop to drop the cookie dough onto your prepared cookie sheet 2 inches apart.
Bake at 350°F for 11 minutes or until the edges are set but the centers are still gooey. Allow to cool for 10 minutes on the baking sheet until set. Enjoy!