In a small/medium bowl, melt the butter in the microwave for 15-30 seconds, and let it cool slightly.
Mix in the brown sugar, cane sugar, vanilla extract, baking soda, salt, and egg yolk.
Lightly mix in the flour just until you don't see any more streaks of flour.
Fold in the mini chocolate chips. It may be easier to use your hand to mix them in.
Place the cookie dough in between two large sheets of parchment paper, and roll it out to about 1/4 inch thick.
Cut the cookie dough into a square large enough to fit inside the basket of your air fryer, and optionally pre-score the dough using a pizza cutter or sharp knife. Reserve the left over dough to make your second batch.
Pre-heat the air fryer to 325°F (163°C).
Cut the excess parchment paper around the cookie dough, leaving about 1 inch around.
Once the air fryer is pre-heated, place the cookie dough with parchment paper inside the basket, and bake on the air fry setting for 5 minutes.
While the dough is baking, grab more parchment paper, roll out your second batch, and cut it into a square. The left over scraps of dough can be left on the parchment to bake (they make for a delicious, crunchy "taste test" when done).
Carefully remove the first cookie batch from the air fryer (it helps to grab one end of the parchment, tip the basket and gently slide it out onto a counter or cutting board). Let it cool while you bake the second batch.
Bake the second batch for 5 minutes, then gently remove onto a counter or cutting board to cool.
Place a square sheet of parchment paper over the first cookie batch, and carefully flip it over so you can proceed to bake the other side (it helps to use a plate for stability).
Using a pizza cutter or a sharp knife, cut the cookie into 1/2 inch strips, and space them out a bit (you won't have room to space them out too far, but it's also unnecessary to do so).
Place your cookie fries back in the air fryer and bake at 325°F (163°C) for 4 minutes.
Carefully remove them from the air fryer to cool, and follow the same process for the second batch.
Let the cookie fries cool completely so they can get firm and crisp up before enjoying.